21 citations · 55 across the 32 of their papers we have counts for
7 papers · 1 filter
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…
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…
Characterization of -concavity preserved by the Dirichlet heat flow
Kazuhiro Ishige, Paolo Salani, Asuka Takatsu
-concavity is a generalization of power concavity and, actually, the largest available generalization of the notion of concavity. We characterize the -concavities preserved b…
Power concavity and Dirichlet heat flow
Kazuhiro Ishige, Paolo Salani, Asuka Takatsu
We show that log-concavity is the weakest power concavity preserved by the Dirichlet heat flow in -dimensional convex domains, where (indeed, we prove that starting wit…
New characterizations of log-concavity
Kazuhiro Ishige, Paolo Salani, Asuka Takatsu
We introduce a notion of -concavity which largely generalizes the usual concavity. By the use of the notions of closedness under positive scalar multiplication and closedness un…
Power concavity for elliptic and parabolic boundary value problems on rotationally symmetric domains
Kazuhiro Ishige, Paolo Salani, Asuka Takatsu
We study power concavity of rotationally symmetric solutions to elliptic and parabolic boundary value problems on rotationally symmetric domains in Riemannian manifolds. As applica…