2 papers
math.MG2025
Strict concavity properties of cross covariograms
Gabriele Bianchi, Almut Burchard, Lawrence Lin
It is well-known that the cross covariogram of two convex bodies in n dimensions is 1/n-concave on its support. This paper provides conditions for strict 1/n-concavity in dimension…
math.DG2025
On monotonicity of heat kernels: a new example and counterexamples
Almut Burchard, Ãngel D. MartÃnez
We discover a new, non-radial example of a manifold whose heat kernel decreases monotonically along all minimal geodesics. We also classify the flat tori with this monotonicity pro…