Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A discrete Laplace-Beltrami operator for simplicial surfaces   We define a discrete Laplace-Beltrami operator for simplicial surfaces. It
depends only on the intrinsic geometry of the surface and its edge weights are
positive. Our Laplace operator is similar to the well known finite-elements
Laplacian (the so called ``cotan formula'') except that it is based on the
intrinsic Delaunay triangulation of the simplicial surface. This leads to new
definitions of discrete harmonic functions, discrete mean curvature, and
discrete minimal surfaces. The definition of the discrete Laplace-Beltrami
operator depends on the existence and uniqueness of Delaunay tessellations in
piecewise flat surfaces. While the existence is known, we prove the uniqueness.
Using Rippa's Theorem we show that, as claimed, Musin's harmonic index provides
an optimality criterion for Delaunay triangulations, and this can be used to
prove that the edge flipping algorithm terminates also in the setting of
piecewise flat surfaces.

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The categories of this paper are: astro-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: cond-mat
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The categories of this paper are: q-fin
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The categories of this paper are: stat
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-lat
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The categories of this paper are: quant-ph