3 papers
math.DG2025
A priori bounds for geodesic diameter. Part II. Fine connectedness properties of varifolds
Ulrich Menne, Christian Scharrer
For varifolds whose first variation is representable by integration, we introduce the notion of indecomposability with respect to locally Lipschitzian real valued functions. Unlike…
math.DG2024
A priori bounds for geodesic diameter. Part III. A Sobolev-Poincaré inequality and applications to a variety of geometric variational problems
Ulrich Menne, Christian Scharrer
Based on a novel type of Sobolev-Poincaré inequality (for generalised weakly differentiable functions on varifolds), we establish a finite upper bound of the geodesic diameter of…
math.DG2024
A sharp lower bound on the mean curvature integral with critical power for integral varifolds
Ulrich Menne
Part I Weakly differentiable functions Part II PDEs on varifolds 15 Sobolev spaces ... 75 16 Preliminaries ... 82 17 Maximum estimates ... 86 18 Second order flatness of Lebesgue s…