From the 1 of 4 linked papers with an AI index.
4 papers
On The Minkowski Problem With Respect To A Mixed Euclidean-Gaussian Density
Stephanie Mui, Lei Qin, Sinan Wang
The paper introduces a new type of Minkowski problem involving a mixed Euclidean-Gaussian volume and proves the existence of smooth, origin‑symmetric solutions using flow methods a…
To -logconcavity and beyond: Geometric properties of Dirichlet eigenfunctions
Lei Qin, Jin Sun, Kui Wang
We prove that, on a bounded open convex domain , the first Dirichlet eigenfunction of the Laplacian or the Ornstein--Uhlenbeck operator is -logconcave fo…
Log-concavity of solutions of parabolic equations related to the Ornstein-Uhlenbeck operator and applications
Andrea Colesanti, Lei Qin, Paolo Salani
In this paper, we investigate the log-concavity of the kernel for the parabolic Ornstein-Uhlenbeck operator in a bounded, convex domain. Consequently, we get the preservation of th…
Geometric properties of solutions to elliptic PDE's in Gauss space and related Brunn-Minkowski type inequalities
Andrea Colesanti, Lei Qin, Paolo Salani
We prove a Brunn-Minkowski type inequality for the first (nontrivial) Dirichlet eigenvalue of the weighted -operator \[ -Î_{p,γ}u=-\text{div}(|\nabla u|^{p-2} \nabla u)+(x,\na…