Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On existence of hypersurfaces translating by powers of Gauss curvature   In this paper we construct complete convex hypersurfaces in $\mathbb R^{n+1}$
which translate under the flow by powers $\alpha \in (0, \frac1{n+2})$ of the
Gauss curvature. The level set of each solution is asymptotic to a shrinking
soliton for the flow by power $\frac \alpha {1-\alpha}$ of the Gauss curvature
in $\mathbb R^n$. For example, our construction reveals the existence of
translators whose level set converges to the sphere, simplex, hypercube and so
on. The translating solitons exist as a family whose parameters correspond to
Jacobi fields, solutions to linearized equation around the asymptotic profile.

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The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
31
The categories of this paper are: ao-sci
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: econ
5
The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys