In this paper, we first study the locally constrained curvature flow of hypersurfaces in
hyperbolic space, which was introduced by Brendle, Guan and Li (An inverse curvature type …

In this paper, we first introduce quermassintegrals for capillary hypersurfaces in the half-
space. Then we solve the related isoperimetric type problems for the convex capillary …

Volume preserving flow and Alexandrov–Fenchel type inequalities in hyperbolic space Page
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Isoperimetric type problems and Alexandrov–Fenchel type inequalities in the hyperbolic space -
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We prove that the static convexity is preserved along two kinds of locally constrained
curvature flows in hyperbolic space. Using the static convexity of the flow hypersurfaces, we …

In this paper we first establish an optimal Sobolev-type inequality for hypersurfaces in
$\mathbb {H}^ n $(see Theorem 1.1). As an application we obtain hyperbolic Alexandrov …

In this article, we will study the isoperimetric problem by introducing a mean curvature type
flow in the Riemannian manifold endowed with a non-trivial conformal vector field. This flow …

New types of hypersurface flows have been introduced recently with goals to establish
isoperimetric type inequalities in geometry. These flows serve as efficient paths to achieve …

In this paper, we first introduce the quermassintegrals for convex hypersurfaces with
capillary boundary in the unit Euclidean ball ${\mathbb {B}}^{n+ 1} $ and derive its first …

We consider the quermassintegral preserving flow of closed h-convex hypersurfaces in
hyperbolic space with the speed given by any positive power of a smooth symmetric, strictly …