Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Capillary surfaces: stability, index and curvature estimates   In this paper we investigate the connection between the index and the
geometry and topology of capillary surfaces. We prove an index estimate for
compact capillary surfaces immersed in general 3-manifolds with boundary. We
also study noncompact capillary surfaces with finite index and show that, under
suitable curvature assumptions, such surface is conformally equivalent to a
compact Riemann surface with boundary, punctured at finitely many points. We
then prove that a weakly stable capillary surface immersed in a half-space of
$\mathbb{R}^3$ which is minimal or has a contact angle less than or equal to
$\pi/2$ must be a half-plane. Using this uniqueness result we obtain curvature
estimates for strongly stable capillary surfaces immersed in a 3-manifold with
bounded geometry.

31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc