Volume preserving flow and Alexandrov–Fenchel type inequalities in hyperbolic space Page
1 © 2021 European Mathematical Society Published by EMS Press. This work is licensed …

The classical Brunn-Minkowski theory studies the geometry of convex bodies in Euclidean
space by use of the Minkowski sum. It originated from H. Brunn's thesis in 1887 and H …

In this paper, we prove a new Heintze–Karcher type inequality for shifted mean convex
hypersurfaces in hyperbolic space. As applications, we prove an Alexandrov-type theorem …

A fundamental theorem of Liouville asserts that positive entire harmonic functions in
Euclidean spaces must be constant. A remarkable Liouville-type theorem of Caffarelli-Gidas …

We mainly study Pogorelov type C 2 estimates for solutions to the Dirichlet problem of Sum
Hessian equations. We establish respectively Pogorelov type C 2 estimates for k-convex …

Abstract In [23], the first author and the third author introduced and studied the horospherical
p-Minkowski problem for smooth horospherically convex domains in hyperbolic space. In …

Given an oriented immersed hypersurface in hyperbolic space H n+ 1 H^n+1, its Gauss map
is defined with values in the space of oriented geodesics of H n+ 1 H^n+1, which is …

Let (M, g) be an asymptotically hyperbolic manifold with a smooth conformal
compactification. We establish a general correspondence between semilinear elliptic …

The hyperbolic space H^ d can be defined as a pseudo-sphere in the (d+ 1) Minkowski
space-time. In this paper, a Fuchsian group Γ is a group of linear isometries of the Minkowski …

Here we are concerned with the compactness of metrics on the disk with prescribed
Gaussian and geodesic curvatures. We consider a blowing up sequence of metrics and give …