A discrete parametrized surface theory in ℝ3

Tim Hoffmann; Andrew O. Sageman-Furnas; Max Wardetzky

doi:10.1093/imrn/rnw015

A discrete parametrized surface theory in ℝ3

Tim Hoffmann, Andrew O. Sageman-Furnas, Max Wardetzky

Associate Professorship of Geometry I

Georg August Universität Göttingen

Research output: Contribution to journal › Article › peer-review

15 Scopus citations

Abstract

We propose a discrete surface theory in ℝ3 that unites the most prevalent versions of discrete special parametrizations. Our theory encapsulates a large class of discrete surfaces given by a Lax representation and, in particular, the one-parameter associated families of constant curvature surfaces. Our theory is not restricted to integrable geometries, but extends to a general surface theory.

Original language	English
Pages (from-to)	4217-4258
Number of pages	42
Journal	International Mathematics Research Notices
Volume	2017
Issue number	14
DOIs	https://doi.org/10.1093/imrn/rnw015
State	Published - 1 Jul 2017

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abstract = "We propose a discrete surface theory in ℝ3 that unites the most prevalent versions of discrete special parametrizations. Our theory encapsulates a large class of discrete surfaces given by a Lax representation and, in particular, the one-parameter associated families of constant curvature surfaces. Our theory is not restricted to integrable geometries, but extends to a general surface theory.",

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AB - We propose a discrete surface theory in ℝ3 that unites the most prevalent versions of discrete special parametrizations. Our theory encapsulates a large class of discrete surfaces given by a Lax representation and, in particular, the one-parameter associated families of constant curvature surfaces. Our theory is not restricted to integrable geometries, but extends to a general surface theory.

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A discrete parametrized surface theory in ℝ3

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