3 papers
math.AP2026
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…
math.AP2025
Rigidity of weighted manifolds via classification results for semilinear equations
Giulio Ciraolo, Alberto Farina, Troy Petitt
We study model semilinear equations on complete and non-compact weighted Riemannian manifolds with non-negative Bakry-Ãmery Ricci curvature. Our main goal is to classify positive…
math.AP2025
A porous medium equation with rough weights: sharp Widder theory
Gabriele Grillo, Matteo Muratori, Troy Petitt +1
We establish an optimal \emph{Widder theory} for a weighted porous medium equation with rough and inhomogeneous density that may be singular at a point and tends to zero at spatial…