Hardy Chan

From fractional Lane–Emden–Serrin equation—existence, multiplicity and local behaviors via classical ODE—to fractional Yamabe metrics with singularity of “maximal” dimension

Point singularities of solutions to the classical Lane–Emden–Serrin equation have a polyhomogeneous asymptotic expansion whose logarithmic corrections are determined by a first order ODE. Surprisingly, we are able to discover such an ODE for the fractional Lane–Emden–Serrin equat...

Nonlocal Approximation of Minimal Surfaces: Optimal Estimates From Stability

ABSTRACT Minimal surfaces in closed 3‐manifolds are classically constructed via the Almgren‐Pitts approach. The Allen‐Cahn approximation has proved to be a powerful alternative, and Chodosh and Mantoulidis (in Ann. Math. 2020) used it to give a new proof of Yau's conjecture for g...