Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Entropy of systolically extremal surfaces and asymptotic bounds   We find an upper bound for the entropy of a systolically extremal surface, in
terms of its systole. We combine the upper bound with A. Katok's lower bound in
terms of the volume, to obtain a simpler alternative proof of M. Gromov's
asymptotic estimate for the optimal systolic ratio of surfaces of large genus.
Furthermore, we improve the multiplicative constant in Gromov's theorem. We
show that every surface of genus at least 20 is Loewner. Finally, we relate, in
higher dimension, the isoembolic ratio to the minimal entropy.

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The categories of this paper are: q-bio
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
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The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: stat