90 citations · 321 across the 30 of their papers we have counts for
34 papers
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…
On monotonicity of heat kernels: a new example and counterexamples
Almut Burchard, Ángel D. Martínez
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…
Maximizers of nonlocal interactions of Wasserstein type
Almut Burchard, Davide Carazzato, Ihsan Topaloglu
We characterize the maximizers of a functional that involves the minimization of the Wasserstein distance between sets of equal volume. We prove that balls are the only maximizers…
Vanishing Mean Oscillation and Continuity of Rearrangements
Almut Burchard, Galia Dafni, Ryan Gibara
We study the decreasing rearrangement of functions in VMO, and show that for rearrangeable functions, the mapping f -> f* preserves vanishing mean oscillation. Moreover, as a map o…
Extendability and the Operator on the Hartogs Triangle
Almut Burchard, Joshua Flynn, Guozhen Lu +1
In this paper it is shown that the Hartogs triangle in is a uniform domain. This implies that the Hartogs triangle is a Sobolev extension domain. Furtherm…
Mean oscillation bounds on rearrangements
Almut Burchard, Galia Dafni, Ryan Gibara
We use geometric arguments to prove explicit bounds on the mean oscillation for two important rearrangements on . For the decreasing rearrangement of a rearrang…