The hyperbolic combinatorial Yamabe flow on infinite triangulated surfaces has short-time well-posedness under angle and degree bounds, and its extended version is globally well-posed under an integrability condition.
The existence and uniqueness of infinite combinatorial Yamabe flows
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In this paper, we study the combinatorial Yamabe flow on infinite triangulated surfaces in Euclidean background geometry, aiming for solving discrete Yamabe problem on noncompact surfaces. Under suitable conditions, we establish the short-time existence and uniqueness of the flow. We further introduce an extended version of the flow and prove its long-time existence. As an application, we prove the convergence result of the Yamabe flow in the case of hexagonal triangulations of the plane.
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Combinatorial Yamabe flow on infinitely triangulated hyperbolic surfaces
The hyperbolic combinatorial Yamabe flow on infinite triangulated surfaces has short-time well-posedness under angle and degree bounds, and its extended version is globally well-posed under an integrability condition.