Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Locating the first nodal set in higher dimensions   This paper estimates the location and the width of the nodal set of the first
Neumann eigenfunctions on a smooth convex domain $\Omega \subset \mathbb R^n$,
whose length is normalized to be 1 and whose cross-section is contained in a
ball of radius $\epsilon$. In \cite{CJK2009}, an $O(\epsilon)$ bound was
obtained by constructing a coordinate system. In this paper, we present a
simpler method that does not require such a coordinate system. Moreover, in the
special case $n = 2$, we obtain an $O(\epsilon^2)$ bound on the width of the
nodal set, in analogy to the corresponding result in the Dirichlet case
obtained in \cite{GJ1995}.

12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin