As on arXiv
Abstract
This paper studies the combinatorial Yamabe flow on hyperbolic bordered surfaces. We show that the flow exists for all time and converges exponentially fast to conformal factor which produces a hyperbolic surface whose lengths of boundary components are equal to prescribed positive numbers. This provides an algorithm to such problems.
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.
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Prescribing hyperbolic bordered surfaces via combinatorial flows
Topics Yamabe flow, Long-time existence & convergence · Same author Shengyu Li · Shared terms “bordered surfaces”, “hyperbolic bordered”, “combinatorial Yamabe”
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Combinatorial Yamabe flow on infinitely triangulated hyperbolic surfaces
Topics Yamabe flow, Long-time existence & convergence · Shared terms “combinatorial Yamabe”, “hyperbolic surface”
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Combinatorial Calabi flows on surfaces with boundary
Topics Yamabe flow, Long-time existence & convergence · Shared terms “combinatorial Yamabe”, “hyperbolic surface”, “algorithm”
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The existence and uniqueness of infinite combinatorial Yamabe flows
Topics Yamabe flow, Long-time existence & convergence · Shared terms “combinatorial Yamabe”
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Infinite Combinatorial Yamabe Flows in Three Dimensions
Topics Yamabe flow, Long-time existence & convergence · Shared terms “combinatorial Yamabe”
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Generalized Yamabe Flows
Topics Yamabe flow, Long-time existence & convergence
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Infinite-time incompleteness of noncompact Yamabe flow
Topics Yamabe flow, Long-time existence & convergence
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
- 6C.4The Yamabe Problem and Critical Exponents
Conformal changes of scalar curvature, the Yamabe functional, Aubin's threshold and Schoen's solution, concentration compactness and bubbles, and why Perelman's log-Sobolev minimisers always exist.