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Main Title: Discrete Yamabe problem for polyhedral surfaces
Author(s): Kourimska, Hana
Springborn, Boris
Type: Preprint
Abstract: We introduce a new discretization of the Gaussian curvature on piecewise at surfaces. As the prime new feature the curvature is scaled by the factor 1/r2 upon scaling the metric globally with the factor r. We develop a variational principle to tackle the corresponding discrete uniformisation theorem – we show that each piecewise at surface is discrete conformally equivalent to one with constant discrete Gaussian curvature. This surface is in general not unique. We demonstrate uniqueness for particular cases and disprove it in general by providing explicit counterexamples. Special attention is paid to dealing with change of combinatorics.
Subject(s): uniformization
polyhedral surfaces
Gaussian curvature
flat surface
Issue Date: 13-Sep-2019
Date Available: 17-Sep-2019
Language Code: en
DDC Class: 516 Geometrie
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik » FG Geometrie und Visualisierung
Appears in Collections:Technische Universität Berlin » Publications

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Version Item Date Summary
3 10.14279/depositonce-9001.3 2019-10-14 17:36:47.411 Structure of the preprint improved, several typos removed.
1 10.14279/depositonce-9001 2019-09-17 09:20:26.0
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