Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The surface diffusion and the Willmore flow for uniformly regular
  hypersurfaces   We consider the surface diffusion and Willmore flows acting on a general
class of (possibly non-compact) hypersurfaces parameterized over a uniformly
regular reference manifold possessing a tubular neighborhood with uniform
radius. The surface diffusion and Willmore flows each give rise to a
fourth-order quasilinear parabolic equation with nonlinear terms satisfying a
specific singular structure. We establish well-posedness of both flows for
initial surfaces that are $C^{1+\alpha}$-regular and parameterized over a
uniformly regular hypersurface. For the Willmore flow, we also show long-term
existence for initial surfaces which are $C^{1+\alpha}$-close to a sphere, and
we prove that these solutions become spherical as time goes to infinity.

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The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: physics