Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Level sets of certain Neumann eigenfunctions under deformation of
  Lipschitz domains. Application to the Extended Courant Property   In this paper, we prove that the Extended Courant Property fails to be true
for certain smooth, strictly convex domains with Neumann boundary condition:
there exists a linear combination of a second and a first Neumann
eigenfunctions, with three nodal domains. For the proof, we revisit a
deformation argument of Jerison and Nadirashvili (J. Amer. Math. Soc. 2000,
vol. 13). This argument being interesting in itself, we give full details. In
particular, we carefully control the dependence of the constants on the
geometry of our Lipschitz domains along the deformations.

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The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
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The categories of this paper are: econ
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
30
The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
9
The categories of this paper are: nlin