4 papers · 1 filter
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…
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…
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…
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…