Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Simplicial Ricci Flow   We construct a discrete form of Hamilton's Ricci flow (RF) equations for a
d-dimensional piecewise flat simplicial geometry, S. These new algebraic
equations are derived using the discrete formulation of Einstein's theory of
general relativity known as Regge calculus. A Regge-Ricci flow (RRF) equation
is naturally associated to each edge, L, of a simplicial lattice. In defining
this equation, we find it convenient to utilize both the simplicial lattice, S,
and its circumcentric dual lattice, S*. In particular, the RRF equation
associated to L is naturally defined on a d-dimensional hybrid block connecting
$\ell$ with its (d-1)-dimensional circumcentric dual cell, L*. We show that
this equation is expressed as the proportionality between (1) the simplicial
Ricci tensor, Rc_L, associated with the edge L in S, and (2) a certain volume
weighted average of the fractional rate of change of the edges, lambda in L*,
of the circumcentric dual lattice, S*, that are in the dual of L. The inherent
orthogonality between elements of S and their duals in S* provide a simple
geometric representation of Hamilton's RF equations. In this paper we utilize
the well established theories of Regge calculus, or equivalently discrete
exterior calculus, to construct these equations. We solve these equations for a
few illustrative examples.

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The categories of this paper are: nucl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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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: physics
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The categories of this paper are: atom-ph