7 papers
Sharp regularity results for eikonal equations in Banach spaces
Trí Minh Lê, Sebastián Tapia-García
Viscosity solutions of eikonal equations need not enjoy regularity beyond Lipschitz continuity. In contrast, differentiable solutions exhibit stronger structural properties. In the…
Impossibility of a nontrivial Brunn--Minkowski inequality for higher Dirichlet eigenvalue
Trí Minh Lê, Khai-Hoan Nguyen-Dang
Let be the th Dirichlet eigenvalue of a convex body . It is well known that satisfies a Brunn--Minkowski inequality: is concave on th…
A note on absolutely minimal extensions in finite metric spaces
Alberto Domínguez Corella, Trí Minh Lê
Absolutely minimal Lipschitz extensions (AMLEs) are known to exist in many infinite metric settings, but the finite case is less settled. In metric spaces with at most four points,…
Power-law asymptotics of fractional polar projection bodies
Trí Minh Lê
The notion of --fractional polar projection bodies, recently introduced by Haddad and Ludwig (Math.\ Ann.\ \textbf{388}:1091--1115, 2024), provides a bridge between fracti…
Computing intrinsic volumes of sublevel sets and applications
Trí Minh Lê, Khai-Hoan Nguyen-Dang
Intrinsic volumes are fundamental geometric invariants generalizing volume, surface area, and mean width for convex bodies. We establish a unified Laplace-Grassmannian representati…
On (discounted) global Eikonal equations in metric spaces
Trí Minh Lê, Sebastián Tapia-García
Eikonal equations in metric spaces have strong connections with the local slope operator (or the De Giorgi slope). In this manuscript, we explore and delve into an analogous model…
On the growth of nonconvex functionals at strict local minimizers
Alberto Domínguez Corella, Trí Minh Lê
We give new characterizations of growth conditions at strict local minimizers. The main characterizations are a variant of the so-called tilt stability property and an analog of th…