Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ricci Flow and Volume Renormalizability   With respect to any special boundary defining function, a conformally compact
asymptotically hyperbolic metric has an asymptotic expansion near its conformal
infinity. If this expansion is even to a certain order and satisfies one extra
condition, then it is possible to define its renormalized volume and show that
it is independent of choices that preserve this evenness structure. We prove
that such expansions are preserved under normalized Ricci flow. We also study
the variation of curvature functionals in this setting, and as one application,
obtain the variation formula $$ \frac{{\rm d}}{{\rm d}t} {\rm RenV}\big(M^n,
g(t)\big) = -\mathop{\vphantom{T}}^R \! \! \! \int_{M^n} (S(g(t))+n(n-1)) {\rm
d}V_{g(t)},$$ where $S(g(t))$ is the scalar curvature for the evolving metric
$g(t)$, and $\mathop{\vphantom{T}}^R \! \! \! \int (\cdot) {\rm d}V_g$ is Riesz
renormalization. This extends our earlier work to a broader class of metrics.

32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess