6 papers
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 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…
Fractional Dirichlet problems with an overdetermined nonlocal Neumann condition
Michele Gatti, Julian Scheuer, Tobias Weth
We investigate symmetry and quantitative approximate symmetry for an overdetermined problem related to the fractional torsion equation in a regular open, bounded set $Ω\subseteq \…
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,…
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 $…