منابع مشابه
Ricci Surfaces
A Ricci surface is a Riemannian 2-manifold (M, g) whose Gaussian curvature K satisfies K∆K+g(dK, dK)+4K = 0. Every minimal surface isometrically embedded in R is a Ricci surface of non-positive curvature. At the end of the 19 century Ricci-Curbastro has proved that conversely, every point x of a Ricci surface has a neighborhood which embeds isometrically in R as a minimal surface, provided K(x)...
متن کاملHarmonic Ricci Flow on surfaces
Let g(t) be a family of smooth Riemannian metrics on an n-dimensional closed manifold M . Moreover, given a smooth closed Riemannian manifold (N, gN ) of arbitrary dimension, let φ(t) be a family of smooth maps from M to N . Then (g(t), φ(t)) is called a solution of the volume preserving Harmonic Ricci Flow (or Ricci Flow coupled with Harmonic Map Heat Flow), if it satisfies ∂tg = −2 Ricg + ...
متن کاملCombinatorial Ricci Flows on Surfaces
We show that the analogue of Hamilton’s Ricci flow in the combinatorial setting produces solutions which converge exponentially fast to Thurston’s circle packing on surfaces. As a consequence, a new proof of Thurston’s existence of circle packing theorem is obtained. As another consequence, Ricci flow suggests a new algorithm to find circle packings.
متن کاملRicci Yang-mills Flow on Surfaces
Abstract. We study the behaviour of the Ricci Yang-Mills flow for U(1) bundles on surfaces. We show that existence for the flow reduces to a bound on the isoperimetric constant. In the presence of such a bound, we show that on S, if the bundle is nontrivial, the flow exists for all time. For higher genus surfaces the flow always exists for all time. The volume normalized flow always exists for ...
متن کاملNormalized Ricci Flow on Nonparabolic Surfaces
This paper studies normalized Ricci flow on a nonparabolic surface, whose scalar curvature is asymptotically −1 in an integral sense. By a method initiated by R. Hamilton, the flow is shown to converge to a metric of constant scalar curvature −1. A relative estimate of Green’s function is proved as a tool.
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ژورنال
عنوان ژورنال: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
سال: 2015
ISSN: 2036-2145,0391-173X
DOI: 10.2422/2036-2145.201206_007