Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantitative Stratification and the Regularity of Harmonic Map Flow   In this paper, we prove estimates and quantitative regularity results for the
harmonic map flow. First, we consider H^1_loc-maps u defined on a parabolic
ball P\subset M\times R and with target manifold N, that have bounded
Dirichlet-energy and Struwe-energy. We define a quantitative stratification,
which groups together points in the domain into quantitative weakly singular
strata S^j_{\eta,r}(u) according to the number of approximate symmetries of u
at certain scales, and prove that their tubular neighborhoods have small
volume, namely Vol(T_r(\cS^j_{\eta,r}(u))< Cr^{m+2-j-\eps}. In particular, this
generalizes the known Hausdorff estimate dim S^j(u)< j for the weakly singular
strata of suitable weak solutions of the harmonic map flow. As an application,
specializing to Chen-Struwe solutions with target manifolds that do not admit
certain harmonic and quasi-harmonic spheres, we obtain refined Minkowski
estimates for the singular set. This generalizes a result of Lin-Wang. We also
obtain L^p-estimates for the reciprocal of the regularity scale. The results
are analogous to our results for mean curvature flow that we recently proved.

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The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
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The categories of this paper are: adap-org
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: chem-ph