Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new class of discrete conformal structures on surfaces with boundary   We introduce a new class of discrete conformal structures on surfaces with
boundary, which have nice interpolations in 3-dimensional hyperbolic geometry.
Then we prove the global rigidity of the new discrete conformal structures
using variational principles, which is a complement of Guo-Luo's rigidity of
the discrete conformal structures and Guo's rigidity of vertex scaling on
surface with boundary. As a result, new convexities of the volume of
generalized hyperbolic pyramids with right-angled hyperbolic hexagonal bases
are obtained. Motivated by Chow-Luo's combinatorial Ricci flow and Luo's
combinatorial Yamabe flow on closed surfaces, we further introduce
combinatorial Ricci flow and combinatorial Calabi flows to deform the new
discrete conformal structures on surfaces with boundary. The basic properties
of these combinatorial curvature flows are established. These combinatorial
curvature flows provide effective algorithms for constructing hyperbolic
metrics on surfaces with totally geodesic boundary components of prescribed
lengths.

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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: q-fin