Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Curvature bound for curve shortening flow via distance comparison and a
  direct proof of Grayson's theorem   A new isoperimetric estimate is proved for embedded closed curves evolving by
curve shortening flow, normalized to have total length $2\pi$. The estimate
bounds the length of any chord from below in terms of the arc length between
its endpoints and elapsed time. Applying the estimate to short segments we
deduce directly that the maximum curvature decays exponentially to 1. This
gives a self-contained proof of Grayson's theorem which does not require the
monotonicity formula or the classification of singularities.

13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
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The categories of this paper are: econ
27
The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol