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math.AP2025
A constant rank theorem for linear elliptic equations on the sphere with applications to the mixed Christoffel problem
A. Colesanti, M. Focardi, P. Guan +1
We study the mixed Christoffel problem for convex bodies providing sufficient conditions for its solution. Key to our approach is a constant rank theorem, following the a…
math.AP2025
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 \[ -Δ_{p,γ}u=-\text{div}(|\nabla u|^{p-2} \nabla u)+(x,\nabl…