Guofang Wei
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Guofang Wei has a total of 57 co-authors. Here are the top co-authors by number of shared publications:
- Xianzhe Dai
Department of Mathematics, University of California, Santa Barbara, California 93106
17 shared publications - Christina Sormani
CUNY Graduate Center and Lehman College, New York, USA
8 shared publications - Xuan Hien Nguyen
Iowa State University, Ames, USA
7 shared publications - Alina Stancu
Department of Mathematics and Statistics, Concordia University, Montreal, Canada
6 shared publications - Julie Clutterbuck
School of Mathematics, Monash University, Melbourne, Australia
6 shared publications - Theodora Bourni
Department of Mathematics, University of Tennessee Knoxville, Knoxville, USA
6 shared publications
Latest Publications
- 7 March 2026
- Published by World Scientific Pub Co Pte Ltd in Communications in Contemporary Mathematics
Singular metrics with non-negative scalar curvature and RCD
We show that a uniformly Euclidean metric with isolated singularity on closed [ ], where [ ] or [ ], [ ] spin, and non-negative scalar curvature on the smooth part is flat and extends smoothly over the singularity. This confirms Schoen’s Conjecture in these cases. The novel approach here, which is the key to the proof, is to show that the space has non-negative synthetic Ricci curvature, i.e. an [ ] space. Our result also holds when the singular set consists of a finite union of submanifolds (of possibly different dimensions) intersecting transversally under additional assumption on the co-dimension and the location of the singular set.
- 7 March 2026
- Published by World Scientific Pub Co Pte Ltd in Communications in Contemporary Mathematics
Singular metrics with non-negative scalar curvature and RCD
We show that a uniformly Euclidean metric with isolated singularity on closed [ ], where [ ] or [ ], [ ] spin, and non-negative scalar curvature on the smooth part is flat and extends smoothly over the singularity. This confirms Schoen’s Conjecture in these cases. The novel approach here, which is the key to the proof, is to show that the space has non-negative synthetic Ricci curvature, i.e. an [ ] space. Our result also holds when the singular set consists of a finite union of submanifolds (of possibly different dimensions) intersecting transversally under additional assumption on the co-dimension and the location of the singular set.
- Open Access
Super Log-concavity of the First Eigenfunctions for Horo-convex Domains in Hyperbolic Space
In this paper, we prove that the first eigenfunction of the Laplacian for a horo-convex domain $Ω\subset\mathbb H^n$ is super log-concave when $\text{diam}(Ω)$ is not large. Our result is optimal in the sense that there are counterexamples %are constructed for the cases when $Ω$ is not horo-convex or when $\text{diam}(Ω)$ is large respectivelyOpen AccessSuper Log-concavity of the First Eigenfunctions for Horo-convex Domains in Hyperbolic Space
In this paper, we prove that the first eigenfunction of the Laplacian for a horo-convex domain $Ω\subset\mathbb H^n$ is super log-concave when $\text{diam}(Ω)$ is not large. Our result is optimal in the sense that there are counterexamples %are constructed for the cases when $Ω$ is not horo-convex or when $\text{diam}(Ω)$ is large respectively - Open Access
- 30 November 2024
- Published by Springer Nature in Mathematische Zeitschrift
- Vol. 309 (1) , 1-17
Finite diffeomorphism theorem for manifolds with lower Ricci curvature and bounded energy
In this paper we prove that the space $$\mathcal {M}(n,\textrm{v},D,\Lambda ):=\{(M^n,g) \text { closed }: ~~\textrm{Ric}\ge -(n-1),~\textrm{Vol}(M)\ge \textrm{v}>0, \text {diam}(M)\le D \text { and } \int _{M}|\textrm{Rm}|^{n/2}\le \Lambda \}$$ has at most $$C(n,\textrm{v},D,\Lambda )$$ many diffeomorphism types. This removes the upper Ricci curvature bound of Anderson-Cheeger’s finite diffeomorphism theorem in Anderson and Cheeger (Geom Funct Anal 1(3):231–252, 1991). Furthermore, if M is Kähler surface, the Riemann curvature $$L^2$$ bound could be replaced by the scalar curvature $$L^2$$ bound.- 30 November 2024
- Published by Springer Nature in Mathematische Zeitschrift
- Vol. 309 (1) , 1-17
Open AccessFinite diffeomorphism theorem for manifolds with lower Ricci curvature and bounded energy
In this paper we prove that the space $$\mathcal {M}(n,\textrm{v},D,\Lambda ):=\{(M^n,g) \text { closed }: ~~\textrm{Ric}\ge -(n-1),~\textrm{Vol}(M)\ge \textrm{v}>0, \text {diam}(M)\le D \text { and } \int _{M}|\textrm{Rm}|^{n/2}\le \Lambda \}$$ has at most $$C(n,\textrm{v},D,\Lambda )$$ many diffeomorphism types. This removes the upper Ricci curvature bound of Anderson-Cheeger’s finite diffeomorphism theorem in Anderson and Cheeger (Geom Funct Anal 1(3):231–252, 1991). Furthermore, if M is Kähler surface, the Riemann curvature $$L^2$$ bound could be replaced by the scalar curvature $$L^2$$ bound. - Open Access
Volume entropy and rigidity for RCD-spaces
We develop the barycenter technique of Besson--Courtois--Gallot so that it can be applied on RCD metric measure spaces. Given a continuous map $f$ from a non-collapsed RCD$(-(N-1),N)$ space $X$ without boundary to a locally symmetric $N$-manifold we show a version of BCG's entropy-volume inequality. The lower bound involves homological and homotopical indices which we introduce. We prove that when equality holds and these indices coincide $X$ is a locally symmetric manifold, and $f$ is homotopic to a Riemannian covering whose degree equals the indices. Moreover, we show a measured Gromov--Hausdorff stability of $X$ and $Y$ involving the homotopical invariant. As a byproduct, we extend a Lipschitz volume rigidity result of Li--Wang to RCD$(K,N)$ spaces without boundary. Finally, we include an application of these methods to the study of Einstein metrics on $4$-orbifolds.Open AccessVolume entropy and rigidity for RCD-spaces
We develop the barycenter technique of Besson--Courtois--Gallot so that it can be applied on RCD metric measure spaces. Given a continuous map $f$ from a non-collapsed RCD$(-(N-1),N)$ space $X$ without boundary to a locally symmetric $N$-manifold we show a version of BCG's entropy-volume inequality. The lower bound involves homological and homotopical indices which we introduce. We prove that when equality holds and these indices coincide $X$ is a locally symmetric manifold, and $f$ is homotopic to a Riemannian covering whose degree equals the indices. Moreover, we show a measured Gromov--Hausdorff stability of $X$ and $Y$ involving the homotopical invariant. As a byproduct, we extend a Lipschitz volume rigidity result of Li--Wang to RCD$(K,N)$ spaces without boundary. Finally, we include an application of these methods to the study of Einstein metrics on $4$-orbifolds. - Open Access
Finite Diffeomorphism Theorem for manifolds with lower Ricci curvature and bounded energy
In this paper we prove that the space $\cM(n,\rv,D,Λ):=\{(M^n,g) \text{ closed }: ~~\Ric\ge -(n-1),~\Vol(M)\ge \rv>0, \diam(M)\le D \text{ and } \int_{M}|\Rm|^{n/2}\le Λ\}$ has at most $C(n,\rv,D,Λ)$ many diffeomorphism types. This removes the upper Ricci curvature bound of Anderson-Cheeger's finite diffeomorphism theorem in \cite{AnCh}. Furthermore, if $M$ is Kähler surface, the Riemann curvature $L^2$ bound could be replaced by the scalar curvature $L^2$ bound.Open AccessFinite Diffeomorphism Theorem for manifolds with lower Ricci curvature and bounded energy
In this paper we prove that the space $\cM(n,\rv,D,Λ):=\{(M^n,g) \text{ closed }: ~~\Ric\ge -(n-1),~\Vol(M)\ge \rv>0, \diam(M)\le D \text{ and } \int_{M}|\Rm|^{n/2}\le Λ\}$ has at most $C(n,\rv,D,Λ)$ many diffeomorphism types. This removes the upper Ricci curvature bound of Anderson-Cheeger's finite diffeomorphism theorem in \cite{AnCh}. Furthermore, if $M$ is Kähler surface, the Riemann curvature $L^2$ bound could be replaced by the scalar curvature $L^2$ bound. - Open Access
Examples of open manifolds with positive Ricci curvature and non-proper Busemann functions
We give the first example of an open manifold with positive Ricci curvature and a non-proper Busemann function at a point. This provides counterexamples to a longtime well-known open question whether the Busemann function at a point of an open manifold with nonnegative Ricci curvature is proper.
Open AccessExamples of open manifolds with positive Ricci curvature and non-proper Busemann functions
We give the first example of an open manifold with positive Ricci curvature and a non-proper Busemann function at a point. This provides counterexamples to a longtime well-known open question whether the Busemann function at a point of an open manifold with nonnegative Ricci curvature is proper.
- Open Access
- 29 August 2023
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society, Series B
- Vol. 10 (34) , 1212-1253
Singular Weyl’s law with Ricci curvature bounded below
We establish two surprising types of Weyl’s laws for some compact RCD ( K , N ) \operatorname {RCD}(K, N) /Ricci limit spaces. The first type could have power growth of any order (bigger than one). The other one has an order corrected by logarithm similar to some fractals even though the space is 2-dimensional. Moreover the limits in both types can be written in terms of the singular sets of null capacities, instead of the regular sets. These are the first examples with such features for RCD ( K , N ) \operatorname {RCD}(K,N) spaces. Our results depend crucially on analyzing and developing important properties of the examples constructed in Pan and Wei [Geom. Funct. Anal. 32 (2022), pp. 676–685], showing them isometric to the α \alpha -Grushin halfplanes. Of independent interest, this also allows us to provide counterexamples to conjectures in Cheeger and Colding [J. Differential Geom. 46 (1997), pp. 406–480] and Kapovitch, Kell, and Ketterer [Math. Z. 301 (2022), pp. 3469–3502].
- 29 August 2023
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society, Series B
- Vol. 10 (34) , 1212-1253
Open AccessSingular Weyl’s law with Ricci curvature bounded below
We establish two surprising types of Weyl’s laws for some compact RCD ( K , N ) \operatorname {RCD}(K, N) /Ricci limit spaces. The first type could have power growth of any order (bigger than one). The other one has an order corrected by logarithm similar to some fractals even though the space is 2-dimensional. Moreover the limits in both types can be written in terms of the singular sets of null capacities, instead of the regular sets. These are the first examples with such features for RCD ( K , N ) \operatorname {RCD}(K,N) spaces. Our results depend crucially on analyzing and developing important properties of the examples constructed in Pan and Wei [Geom. Funct. Anal. 32 (2022), pp. 676–685], showing them isometric to the α \alpha -Grushin halfplanes. Of independent interest, this also allows us to provide counterexamples to conjectures in Cheeger and Colding [J. Differential Geom. 46 (1997), pp. 406–480] and Kapovitch, Kell, and Ketterer [Math. Z. 301 (2022), pp. 3469–3502].
- Open Access
Modulus of Concavity and Fundamental Gap Estimates on Surfaces
The fundamental gap of a domain is the difference between the first two eigenvalues of the Laplace operator. In a series of recent and celebrated works, it was shown that for convex domains in $\mathbb R^n$ and $\mathbb S^n$ with Dirichlet boundary condition the fundamental gap is at least $\frac{3 π^2}{D^2}$ where $D$ denotes the diameter of the domain. The key to these results is to establish a strong concavity estimate for the logarithm of the first eigenfunction. In this article, we prove corresponding log-concavity and fundamental gap estimates for surfaces with non-constant positive curvature via a two-point maximum principle. However, the curvature not being constant greatly increases the difficulty of the computation.Open AccessModulus of Concavity and Fundamental Gap Estimates on Surfaces
The fundamental gap of a domain is the difference between the first two eigenvalues of the Laplace operator. In a series of recent and celebrated works, it was shown that for convex domains in $\mathbb R^n$ and $\mathbb S^n$ with Dirichlet boundary condition the fundamental gap is at least $\frac{3 π^2}{D^2}$ where $D$ denotes the diameter of the domain. The key to these results is to establish a strong concavity estimate for the logarithm of the first eigenfunction. In this article, we prove corresponding log-concavity and fundamental gap estimates for surfaces with non-constant positive curvature via a two-point maximum principle. However, the curvature not being constant greatly increases the difficulty of the computation. - Open Access
Singular Weyl's law with Ricci curvature bounded below
We establish two surprising types of Weyl's laws for some compact $\mathrm{RCD}(K, N)$/Ricci limit spaces. The first type could have power growth of any order (bigger than one). The other one has an order corrected by logarithm similar to some fractals even though the space is 2-dimensional. Moreover the limits in both types can be written in terms of the singular sets of null capacities, instead of the regular sets. These are the first examples with such features for $\mathrm{RCD}(K,N)$ spaces. Our results depends crucially on analyzing and developing important properties of the examples constructed by the last two authors, showing them isometric to the $\alpha$-Grushin halfplanes. Of independent interest, this also allows us to provide counterexamples to conjectures by Cheeger-Colding and by Kapovitch-Kell-Ketterer.Open AccessSingular Weyl's law with Ricci curvature bounded below
We establish two surprising types of Weyl's laws for some compact $\mathrm{RCD}(K, N)$/Ricci limit spaces. The first type could have power growth of any order (bigger than one). The other one has an order corrected by logarithm similar to some fractals even though the space is 2-dimensional. Moreover the limits in both types can be written in terms of the singular sets of null capacities, instead of the regular sets. These are the first examples with such features for $\mathrm{RCD}(K,N)$ spaces. Our results depends crucially on analyzing and developing important properties of the examples constructed by the last two authors, showing them isometric to the $\alpha$-Grushin halfplanes. Of independent interest, this also allows us to provide counterexamples to conjectures by Cheeger-Colding and by Kapovitch-Kell-Ketterer. - 5 December 2022
- Published by Mathematical Sciences Publishers in Analysis & PDE
- Vol. 15 (7) , 1703-1724
Eigenvalue estimates for Kato-type Ricci curvature conditions
- 5 December 2022
- Published by Mathematical Sciences Publishers in Analysis & PDE
- Vol. 15 (7) , 1703-1724
Eigenvalue estimates for Kato-type Ricci curvature conditions