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Non-homogeneous curvature flows in hyperbolic space
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^{beta}r; we treat both regimes: beta>1+k{alpha} and beta=1+k{alpha}. 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.
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BibTeX
@misc{sheng2026nonhomogeneous,
title = {{Non-homogeneous curvature flows in hyperbolic space}},
author = {Hongyi Sheng and Weimin Sheng and Jiazhuo Yang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.29199},
eprint = {2609.29199},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.29199},
}
RIS
TY - UNPB
TI - Non-homogeneous curvature flows in hyperbolic space
AU - Hongyi Sheng
AU - Weimin Sheng
AU - Jiazhuo Yang
PY - 2026
DA - 2026/09/24
PB - arXiv
DO - 10.48550/arxiv.2609.29199
UR - https://arxiv.org/abs/2609.29199
AB - 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^{beta}r; we treat both regimes: beta>1+k{alpha} and beta=1+k{alpha}. 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.
ER -