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math.DG2025
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,…
math.DG2025
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…
math.DG2025
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 -…