7 citations · 8 across the 15 of their papers we have counts for
15 papers
Contracting Transport Maps on Riemannian Manifolds
Shrey Aryan, Bang-Xian Han, Zhuo-Nan Zhu
We use inverse mean curvature flow to construct bi-Lipschitz maps that preserve normalized volume and decrease distances. These maps send a round sphere onto any smooth closed stri…
Topological Half-Space Theorems for Minimal Hypersurfaces in
Shrey Aryan, Alexander D. McWeeney
The three-dimensional catenoid in is a complete embedded minimal hypersurface contained in a slab, showing that the half-space theorem does not extend directly to hi…
Calabi-Yau Conjecture for Minimal Hypersurfaces in with bounded geometry
Shrey Aryan, Alexander D. McWeeney, Giuseppe Tinaglia
The Calabi-Yau conjectures for complete minimal hypersurfaces for ask whether a complete minimal hypersurface must be unbounded, and more…
Non-uniqueness of geodesic limits and a question of Grayson and Gage
Shrey Aryan, Tang-Kai Lee
Grayson and Gage proved that an immortal curve shortening flow of simple closed curves on a closed surface converges subsequentially to a closed geodesic, and they asked whether th…
Spectral Obstructions to Contracting Transport Maps on Curved Spaces
Shrey Aryan
Caffarelli's contraction theorem states that the Brenier optimal transport map from the standard Gaussian measure to a more log-concave probability measure is -Lipschitz. Motiva…
On the Calabi-Yau Conjectures for Minimal Hypersurfaces in Higher Dimensions
Shrey Aryan, Alexander D. McWeeney
In this paper, we study the Calabi-Yau conjectures for complete minimal hypersurfaces in dimensions . These conjectures ask whether a comple…
Continuous-in-time Bubbling for the Energy-Critical Heat Flow
Shrey Aryan
We show that any finite energy solution of the energy-critical nonlinear heat flow in dimensions asymptotically resolves into a sum of possibly time-dependent solitons, a…
Entropic Selection Principle for Monge's Optimal Transport
Shrey Aryan, Promit Ghosal
We investigate the small regularization limit of entropic optimal transport when the cost function is the Euclidean distance in dimensions , and the marginal measures are ab…
Free energy minimizers with radial densities: classification and quantitative stability
Shrey Aryan, Lauro Silini
We study the isoperimetric problem with a potential energy in weighted by a radial density and analyze the geometric properties of minimizers. Notably, we co…
Improvement of Wu's logarithmic Sobolev inequality via the Poisson-Föllmer process
Shrey Aryan, Pablo López-Rivera, Yair Shenfeld
We give an alternative proof to Wu's logarithmic Sobolev inequality for the Poisson measure on the nonnegative integers using a stochastic variational formula for entropy. We show…
Soliton resolution for the energy-critical nonlinear heat equation in the radial case
Shrey Aryan
We establish the Soliton Resolution Conjecture for the radial critical non-linear heat equation in dimension Thus, every finite energy solution resolves, continuously in…
Concavity for elliptic and parabolic equations in locally symmetric spaces with nonnegative curvature
Shrey Aryan, Michael B. Law
We establish a concavity principle for solutions to elliptic and parabolic equations on locally symmetric spaces with nonnegative sectional curvature, extending the results of Lang…
Trend to equilibrium for flows with random diffusion
Shrey Aryan, Matthew Rosenzweig, Gigliola Staffilani
Motivated by the possibility of noise to cure equations of finite-time blowup, recent work arXiv:2109.09892 by the second and third named authors showed that with quantifiable high…
Stability of Hardy Littlewood Sobolev Inequality under Bubbling
Shrey Aryan
In this note we will generalize the results deduced in arXiv:1905.08203 and arXiv:2103.15360 to fractional Sobolev spaces. In particular we will show that for , …
Existence of two-solitary waves with logarithmic distance for the nonlinear Klein-Gordon equation
Shrey Aryan
We consider the…