19 citations · 69 across the 31 of their papers we have counts for
4 papers · 2 filters
A Brunn--Minkowski inequality and Convexity for the 2-Hessian eigenvalue in convex domains
Jiahuan Li, Xi-Nan Ma, Guohuan Qiu +1
We prove the strict log-concavity of the positive first eigenfunction \(-u\) of the \(2\)-Hessian equation and the strict -convexity of the solution for the corresponding tors…
A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain
Jiahuan Li, Xi-Nan Ma, Paolo Salani
We use the deformation methods to obtain the strictly log concavity of solution of a class Hessian equation in bounded convex domain in , as an application we get t…
Preservation of F-convexity under the heat flow
Kazuhiro Ishige, Troy Petitt, Paolo Salani
We introduce the notion of F-convexity as a general extension of power convexity. We characterize the F-convexities preserved under the heat flow in the n-dimensional Euclidean spa…
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…