A Metric for genus-zero surfaces

Joel Hass; Patrice Koehl

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arXiv · 1507.00798

A Metric for genus-zero surfaces

Joel Hass·Patrice Koehl

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Abstract

We present a new method to compare the shapes of genus-zero surfaces. We introduce a measure of mutual stretching, the symmetric distortion energy, and establish the existence of a conformal diffeomorphism between any two genus-zero surfaces that minimizes this energy. We then prove that the energies of the minimizing diffeomorphisms give a metric on the space of genus-zero Riemannian surfaces. This metric and the corresponding optimal diffeomorphisms are shown to have properties that are highly desirable for applications.

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BibTeX RIS

Joel Hass, Patrice Koehl. 2015-07-03. A Metric for genus-zero surfaces. https://arxiv.org/abs/1507.00798

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