As on arXiv
Abstract
Let H^n+1 be hyperbolic space of sectional curvature -1, with a fixed point o. We study the non-homogeneous curvature flow X_t=-f(r) sigma_k^alpha nu of smooth, closed, strictly h-convex hypersurfaces enclosing o, where r is the geodesic distance to o and alpha>0. The radial weight f is modeled on sinh^betar; we treat both regimes: beta>1+kalpha and beta=1+kalpha. Under a structural condition of f, the flow exists smoothly for all time, preserves strict h-convexity, and contracts to o. The normalized radial function converges, exponentially in normalized time: to 1 and to a positive constant R_infty respectively in two different cases.
Comments: 39 pages
Its neighbourhood
Connected papers
The 8 papers on this site closest to this one, judged by the topics they share, the words and phrases in their titles and abstracts, and their authors. They are not its citations, but a map of the work around it. Papers here go back to 2021, plus the canon.
-
Non-homogeneous curvature flows in a hemisphere
Topics Homogeneous spaces, Other curvature flows · Same authors Hongyi Sheng, Weimin Sheng, Jiazhuo Yang · Shared terms “beta kalpha”, “normalized radial”, “hypersurfaces enclosing”
-
Long time behavior of a class of non-homogeneous anisotropic fully nonlinear curvature flows
Topics Homogeneous spaces, Other curvature flows · Same authors Weimin Sheng, Jiazhuo Yang · Shared terms “convex hypersurfaces”, “flow exists”
-
Noncollapsing for Curvature Flows with Inhomogeneous Speeds
Topics Homogeneous spaces, Other curvature flows · Same author Weimin Sheng · Shared terms “structural condition”
-
Contraction of hypersurfaces with positive sectional curvature in hyperbolic space
Topics Homogeneous spaces, Other curvature flows · Shared terms “hyperbolic space”, “sectional curvature”, “contracts”
-
Volume preserving nonhomogeneous Gauss curvature flow in hyperbolic space
Topics Homogeneous spaces, Other curvature flows · Shared terms “hyperbolic space”, “convex hypersurfaces”
-
Flow by Gauss curvature to the -Gaussian Minkowski problem
Topics Other curvature flows · Same author Weimin Sheng · Shared terms “convex hypersurfaces”
-
Non-homothetic convex ancient solutions for flows by high powers of curvature
Topics Homogeneous spaces, Other curvature flows
-
A flow approach to the Musielak-Orlicz-Gauss image problem
Topics Other curvature flows · Same author Weimin Sheng
Read around it
Background reading
The guides for the topics of this paper: what each idea is, why it matters, and the papers to read first.
In the guidebook
- 11A.13Homogeneous Flows
A computable laboratory: the flow on Thurston’s geometries.