46 citations · 460 across the 44 of their papers we have counts for
4 papers · 1 filter
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…
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 \m…
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 -…