Alina Stancu
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
Alina Stancu has a total of 16 co-authors. Here are the top co-authors by number of shared publications:
- Valentina-Mira Wheeler
Institute for Mathematics and Its Applications, University of Wollongong, Wollongong, Australia
7 shared publications - Guofang Wei
Department of Mathematics, University of California, Santa Barbara, CA 93106, USA
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 - Xuan Hien Nguyen
Iowa State University, Ames, USA
6 shared publications - Harald Proppe
Dept. of Mathematics and Statistics, Concordia University, Montreal, Canada
2 shared publications
Latest Publications
- 24 May 2025
- Published by Springer Nature in The Journal of Geometric Analysis
- Vol. 35 (7) , 1-21
A Curvature Flow for Radially Symmetric Hypersurfaces in ${\mathbb {R}}^{n+1}$ by Non-symmetric Speed of their Principal Curvatures- 24 May 2025
- Published by Springer Nature in The Journal of Geometric Analysis
- Vol. 35 (7) , 1-21
A Curvature Flow for Radially Symmetric Hypersurfaces in ${\mathbb {R}}^{n+1}$ by Non-symmetric Speed of their Principal Curvatures- 24 January 2025
- Published by Springer Nature in Acta Mathematica Scientia
- Vol. 45 (1) , 280-290
Characterizations of balls and ellipsoids by infinitesimal homothetic conditions
- 24 January 2025
- Published by Springer Nature in Acta Mathematica Scientia
- Vol. 45 (1) , 280-290
Characterizations of balls and ellipsoids by infinitesimal homothetic conditions
- Open Access
- 1 January 2025
- Published by Banach Press LLC in Journal of Convex Analysis
- Vol. 32 (3) , 723-730
Approximation Approach to Holditch's Theorem
Due to recent results by the authors, Holditch's original proof of his eponymous theorem is effective when applied to a sufficiently smooth convex curve with positive curvature, since such curves were shown to possess a smooth envelope generated by a traveling chord. In the present work, we smoothly approximate a convex curve satisfying only a mild local obtuseness condition, and thereby derive Holditch's theorem for such curves without requiring them to possess an envelope.
- 1 January 2025
- Published by Banach Press LLC in Journal of Convex Analysis
- Vol. 32 (3) , 723-730
Open AccessApproximation Approach to Holditch's Theorem
Due to recent results by the authors, Holditch's original proof of his eponymous theorem is effective when applied to a sufficiently smooth convex curve with positive curvature, since such curves were shown to possess a smooth envelope generated by a traveling chord. In the present work, we smoothly approximate a convex curve satisfying only a mild local obtuseness condition, and thereby derive Holditch's theorem for such curves without requiring them to possess an envelope.
- 3 February 2022
- Published by Springer Nature in Calculus of Variations and Partial Differential Equations
- Vol. 61 (2) , 1-14
Ancient solutions for flow by powers of the curvature in ${\mathbb {R}}^2$- 3 February 2022
- Published by Springer Nature in Calculus of Variations and Partial Differential Equations
- Vol. 61 (2) , 1-14
Ancient solutions for flow by powers of the curvature in ${\mathbb {R}}^2$- 13 September 2021
- Published by Springer Nature in Annales Henri Poincare
- Vol. 23 (2) , 595-614
The Vanishing of the Fundamental Gap of Convex Domains in $\mathbb {H}^n$- 13 September 2021
- Published by Springer Nature in Annales Henri Poincare
- Vol. 23 (2) , 595-614
The Vanishing of the Fundamental Gap of Convex Domains in $\mathbb {H}^n$- 12 July 2021
- Published by Oxford University Press (OUP) in International Mathematics Research Notices
- Vol. 2022 (20) , 16035-16045
The Fundamental Gap of Horoconvex Domains in ℍn
We show that, for horoconvex domains in the hyperbolic space, the product of their fundamental gap with the square of their diameter has no positive lower bound. The result follows from the study of the fundamental gap of geodesic balls as the radius goes to infinity. In the process, we improve the lower bound for the first eigenvalue of balls in hyperbolic space.
- 12 July 2021
- Published by Oxford University Press (OUP) in International Mathematics Research Notices
- Vol. 2022 (20) , 16035-16045
The Fundamental Gap of Horoconvex Domains in ℍn
We show that, for horoconvex domains in the hyperbolic space, the product of their fundamental gap with the square of their diameter has no positive lower bound. The result follows from the study of the fundamental gap of geodesic balls as the radius goes to infinity. In the process, we improve the lower bound for the first eigenvalue of balls in hyperbolic space.
- 1 January 2021
- Published by International Press of Boston in Mathematical Research Letters
- Vol. 28 (5) , 1319-1336
Explicit fundamental gap estimates for some convex domains in $\mathbb{H}^2$- 1 January 2021
- Published by International Press of Boston in Mathematical Research Letters
- Vol. 28 (5) , 1319-1336
Explicit fundamental gap estimates for some convex domains in $\mathbb{H}^2$- 3 June 2020
- Published by Oxford University Press (OUP) in International Mathematics Research Notices
- Vol. 2022 (2) , 1016-1044
Prescribing Centro-Affine Curvature From One Convex Body to Another
We study a curvature flow on smooth, closed, strictly convex hypersurfaces in $\mathbb{R}^n$, which commutes with the action of $SL(n)$. The flow shrinks the initial hypersurface to a point that, if rescaled to enclose a domain of constant volume, is a smooth, closed, strictly convex hypersurface in $\mathbb{R}^n$ with centro-affine curvature proportional, but not always equal, to the centro-affine curvature of a fixed hypersurface. We outline some consequences of this result for the geometry of convex bodies and the logarithmic Minkowski inequality.- 3 June 2020
- Published by Oxford University Press (OUP) in International Mathematics Research Notices
- Vol. 2022 (2) , 1016-1044
Prescribing Centro-Affine Curvature From One Convex Body to Another
We study a curvature flow on smooth, closed, strictly convex hypersurfaces in $\mathbb{R}^n$, which commutes with the action of $SL(n)$. The flow shrinks the initial hypersurface to a point that, if rescaled to enclose a domain of constant volume, is a smooth, closed, strictly convex hypersurface in $\mathbb{R}^n$ with centro-affine curvature proportional, but not always equal, to the centro-affine curvature of a fixed hypersurface. We outline some consequences of this result for the geometry of convex bodies and the logarithmic Minkowski inequality.- Open AccessThe vanishing of the fundamental gap of convex domains in $\mathbb H^n$For the Laplace operator with Dirichlet boundary conditions on convex domains in $\mathbb H^n$, $n\geq 2$, we prove that the product of the fundamental gap with the square of the diameter can be arbitrarily small for domains of any diameter.Open AccessThe vanishing of the fundamental gap of convex domains in $\mathbb H^n$For the Laplace operator with Dirichlet boundary conditions on convex domains in $\mathbb H^n$, $n\geq 2$, we prove that the product of the fundamental gap with the square of the diameter can be arbitrarily small for domains of any diameter.
- Open AccessAncient solutions for flow by powers of the curvature in $\mathbb R^2$We construct a new compact convex embedded ancient solution of the $\kappa^\alpha$ flow in $\mathbb R^2$, $\alpha\in(\frac12,1)$ that lies between two parallel lines. Using this solution we classify all convex ancient solutions of the $\kappa^\alpha$ flow in $\mathbb R^2$, for $\alpha\in(\frac23,1)$. Moreover, we show that any non-compact convex embedded ancient solution of the $\kappa^\alpha$ flow in $\mathbb R^2$, $\alpha\in(\frac12,1)$ must be a translating solution.Open AccessAncient solutions for flow by powers of the curvature in $\mathbb R^2$We construct a new compact convex embedded ancient solution of the $\kappa^\alpha$ flow in $\mathbb R^2$, $\alpha\in(\frac12,1)$ that lies between two parallel lines. Using this solution we classify all convex ancient solutions of the $\kappa^\alpha$ flow in $\mathbb R^2$, for $\alpha\in(\frac23,1)$. Moreover, we show that any non-compact convex embedded ancient solution of the $\kappa^\alpha$ flow in $\mathbb R^2$, $\alpha\in(\frac12,1)$ must be a translating solution.