Xiaonan Ma
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
Xiaonan Ma has a total of 52 co-authors. Here are the top co-authors by number of shared publications:
- George Marinescu
Department Mathematik/Informatik , Abteilung Mathematik , Universität zu Köln , Weyertal 86-90, 50931 Köln , Germany ; and Institute of Mathematics “Simion Stoilow”, Romanian Academy, Bucharest, Romania
38 shared publications - Weiping Zhang
Chern Institute of Mathematics and LPMC, Nankai University, Tianjin, People’s Republic of China
11 shared publications Kefeng Liu
University of California at Los Angeles
9 shared publicationsWeiping Zhang
9 shared publications- Kefeng Liu
Center of Mathematical Science, Zhejiang University and Department of Mathematics, University of California at Los Angeles, CA 90095-1555, USA
6 shared publications - Kefeng Liu
Center of Mathematical Sciences, Zhejiang University, Hangzhou, China
4 shared publications
Latest Publications
- 9 October 2023
- Published by Oxford University Press (OUP) in International Mathematics Research Notices
- Vol. 2024 (8) , 6606-6631
Quillen Metrics and Branched Coverings
We give a formula to compare the Quillen metrics associated to a branched covering from holomorphic line bundles.
- 9 October 2023
- Published by Oxford University Press (OUP) in International Mathematics Research Notices
- Vol. 2024 (8) , 6606-6631
Quillen Metrics and Branched Coverings
We give a formula to compare the Quillen metrics associated to a branched covering from holomorphic line bundles.
- Open Access
Quillen metrics and branched coverings
We give a formula to compare the Quillen metrics associated to a branched covering from holomorphic line bundles.
Open AccessQuillen metrics and branched coverings
We give a formula to compare the Quillen metrics associated to a branched covering from holomorphic line bundles.
- Open Access
Comparison of two equivariant $η$-forms
In this paper, we first define the equivariant infinitesimal $\eta$-form, then we compare it with the equivariant $\eta$-form, modulo exact forms, by a locally computable form. As a consequence, we obtain the singular behavior of the equivariant $\eta$-form, modulo exact forms, as a function on the acting Lie group. This result extends a result of Goette and it plays an important role in our recent work on the localization of $\eta$-invariants and on the differential $K$-theory.
Open AccessComparison of two equivariant $η$-forms
In this paper, we first define the equivariant infinitesimal $\eta$-form, then we compare it with the equivariant $\eta$-form, modulo exact forms, by a locally computable form. As a consequence, we obtain the singular behavior of the equivariant $\eta$-form, modulo exact forms, as a function on the acting Lie group. This result extends a result of Goette and it plays an important role in our recent work on the localization of $\eta$-invariants and on the differential $K$-theory.
- 23 August 2022
- Published by Springer Nature in Mathematische Annalen
- Vol. 386 (3-4) , 2207-2253
Superconnection and family Bergman kernels
- 23 August 2022
- Published by Springer Nature in Mathematische Annalen
- Vol. 386 (3-4) , 2207-2253
Superconnection and family Bergman kernels
- Open Access
- 18 February 2022
- Published by Springer Nature in Mathematische Zeitschrift
- Vol. 301 (3) , 2339-2367
Quotient of Bergman kernels on punctured Riemann surfaces
In this paper we consider a punctured Riemann surface endowed with a Hermitian metric that equals the Poincaré metric near the punctures, and a holomorphic line bundle that polarizes the metric. We introduce a new method to compare the Bergman kernels of high tensor powers of the line bundle and of the Poincaré model near the singularity and show that their quotient tends to one uniformly on a neighborhood of the singularity up to arbitrary negative powers of the tensor power.
- 18 February 2022
- Published by Springer Nature in Mathematische Zeitschrift
- Vol. 301 (3) , 2339-2367
Open AccessQuotient of Bergman kernels on punctured Riemann surfaces
In this paper we consider a punctured Riemann surface endowed with a Hermitian metric that equals the Poincaré metric near the punctures, and a holomorphic line bundle that polarizes the metric. We introduce a new method to compare the Bergman kernels of high tensor powers of the line bundle and of the Poincaré model near the singularity and show that their quotient tends to one uniformly on a neighborhood of the singularity up to arbitrary negative powers of the tensor power.
- 5 November 2021
- Published by Springer Nature in Acta Mathematica Scientia
- Vol. 41 (6) , 1859-1872
Quantization Commutes with Reduction, a Survey
- 5 November 2021
- Published by Springer Nature in Acta Mathematica Scientia
- Vol. 41 (6) , 1859-1872
Quantization Commutes with Reduction, a Survey
- Open Access
Optimal convergence speed of Bergman metrics on symplectic manifolds
It is known that a compact symplectic manifold endowed with a prequantum line bundle can be embedded in the projective space generated by the eigensections of low energy of the Bochner Laplacian acting on high $p$-tensor powers of the prequantum line bundle. We show that the Fubini-Study forms induced by these embeddings converge at speed rate $1/p^{2}$ to the symplectic form. This result implies the generalization to the almost-K\"ahler case of the lower bounds on the Calabi functional given by Donaldson for K\"ahler manifolds, as shown by Lejmi and Keller.Open AccessOptimal convergence speed of Bergman metrics on symplectic manifolds
It is known that a compact symplectic manifold endowed with a prequantum line bundle can be embedded in the projective space generated by the eigensections of low energy of the Bochner Laplacian acting on high $p$-tensor powers of the prequantum line bundle. We show that the Fubini-Study forms induced by these embeddings converge at speed rate $1/p^{2}$ to the symplectic form. This result implies the generalization to the almost-K\"ahler case of the lower bounds on the Calabi functional given by Donaldson for K\"ahler manifolds, as shown by Lejmi and Keller. - Open Access
Geometric quantization on CR manifolds
Let $X$ be a compact connected orientable CR manifold with the action of a connected compact Lie group $G$. Under natural pseudoconvexity assumptions we show that the CR Guillemin-Strernberg map is Fredholm at the level of Sobolev spaces of CR functions. As application we study this map for holomorphic line bundles which are positive near the inverse image of $0$ by the momentum map. We also show that "quantization commutes with reduction" for Sasakian manifolds.Open AccessGeometric quantization on CR manifolds
Let $X$ be a compact connected orientable CR manifold with the action of a connected compact Lie group $G$. Under natural pseudoconvexity assumptions we show that the CR Guillemin-Strernberg map is Fredholm at the level of Sobolev spaces of CR functions. As application we study this map for holomorphic line bundles which are positive near the inverse image of $0$ by the momentum map. We also show that "quantization commutes with reduction" for Sasakian manifolds. - 11 June 2020
- Published by Springer Nature in Inventiones Mathematicae
- Vol. 222 (2) , 545-613
Differential K-theory and localization formula for $\eta $-invariants- 11 June 2020
- Published by Springer Nature in Inventiones Mathematicae
- Vol. 222 (2) , 545-613
Differential K-theory and localization formula for $\eta $-invariants