10 papers · 1 filter
Capillary quermassintegral inequalities in the unit ball
Shujing Pan, Julian Scheuer
This paper is about hypersurfaces with boundary lying in the Euclidean unit ball, which meet the unit sphere at a fixed angle . Such hypersurfaces are called …
Foliation of null cones by surfaces of constant spacetime mean curvature near MOTS
Ben Lambert, Julian Scheuer
Marginally Outer Trapped Surfaces (MOTS) in spacetimes are well-known to indicate the existence of black holes. Using flow techniques, we prove that a neighbourhood of a stable MOT…
The quermassintegral inequalities for horo-convex domains in the sphere
Shujing Pan, Julian Scheuer
We study a new notion of convexity for subsets of the unit sphere, which closely resembles the horo-convexity for subsets of the hyperbolic space. We call this notion, accordingly,…
Two properties of optimisers for the reverse isoperimetric problem
Deniz M. Hamdy, Julian Scheuer
The reverse isoperimetric problem asks for existence and properties of bounded convex sets in a Riemannian manifold which maximise the perimeter under all those sets of fixed volum…
Capillary Christoffel-Minkowski problem
Yingxiang Hu, Mohammad N. Ivaki, Julian Scheuer
The result of Guan and Ma (Invent. Math. 151 (2003)) states that if is spherically convex, then arises as the curvature (the -…
A capillary problem for spacelike mean curvature flow in a cone of Minkowski space
Wilhelm Klingenberg, Ben Lambert, Julian Scheuer
Consider a convex cone in three-dimensional Minkowski space which either contains the lightcone or is contained in it. This work considers mean curvature flow of a proper spacelike…