Showing 2024Show all
3 papers · 1 filter
math.DG2024
A sharp spectral splitting theorem
Gioacchino Antonelli, Marco Pozzetta, Kai Xu
We prove a sharp spectral generalization of the Cheeger--Gromoll splitting theorem. We show that if a complete non-compact Riemannian manifold of dimension has at lea…
math.DG2024
Inverse mean curvature flow with outer obstacle
Kai Xu
We develop a new boundary condition for the weak inverse mean curvature flow, which gives canonical and non-trivial solutions in bounded domains. Roughly speaking, the boundary of…
math.DG2024
New spectral Bishop-Gromov and Bonnet-Myers theorems and applications to isoperimetry
Gioacchino Antonelli, Kai Xu
We show a sharp and rigid spectral generalization of the classical Bishop--Gromov volume comparison theorem: if a closed Riemannian manifold of dimension satisfies…