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math.AP2024
Riemannian starshape and capacitary problems
Kazuhiro Ishige, Paolo Salani, Asuka Takatsu
We prove the Riemannian version of a classical Euclidean result: every level set of the capacitary potential of a starshaped ring is starshaped. In the Riemannian setting, we restr…
math.AP2024
Non-preservation of concavity properties by the Dirichlet heat flow on Riemannian manifolds
Kazuhiro Ishige, Asuka Takatsu, Haruto Tokunaga
We prove that no concavity properties are preserved by the Dirichlet heat flow in a totally convex domain of a Riemannian manifold unless the sectional curvature vanishes everywher…