Work

Gauss curvature type flow and Alexandrov–Fenchel inequalities in the hyperbolic space

Year: 2025

Type: article

Abstract: We consider the Gauss curvature type flow for uniformly convex hypersurfaces in the hyperbolic space [Formula: see text]. We prove that if the initial closed hypersurface is smooth and uniformly convex, then the smooth solution exists for all positive time and converges smoothly and exponentially to a geodesic sphere centered at the origin. The key step is to prove the upper bound of Gauss curvature and that uniform convexity preserves along the flow. As an application, we provide a new proof for an Alexandrov–Fenchel inequality comparing [Formula: see text]th quermassintegral and volume of convex domains in [Formula: see text] [Formula: see text].

Source: Communications in Contemporary Mathematics

DOI: 10.1142/s0219199725500555

Authors: Tianci Luo, Rong Zhou

Institution: University of Science and Technology of China

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Key Research and Development Program of China

Award: G130972461