Topological Properties of Neumann Domains

Autor(en)

Ram Band, David Fajman

Abstrakt

A Laplacian eigenfunction on a two-dimensional manifold dictates some natural partitions of the manifold; the most apparent one being the well studied nodal domain partition. An alternative partition is revealed by considering a set of distinguished gradient flow lines of the eigenfunction - those which are connected to saddle points. These give rise to Neumann domains. We establish complementary definitions for Neumann domains and Neumann lines and use basic Morse homology to prove their fundamental topological properties. We study the eigenfunction restrictions to these domains. Their zero set, critical points and spectral properties allow to discuss some aspects of counting the number of Neumann domains and estimating their geometry.

Organisation(en)

Gravitationsphysik

Externe Organisation(en)

Technion - Israel Institute of Technology

Journal

Annales Henri Poincare

Band

17

Seiten

2379–2407

Anzahl der Seiten

29

ISSN

1424-0637

DOI

https://doi.org/10.1007/s00023-016-0468-7

Publikationsdatum

09-2015

Peer-reviewed

Ja

ÖFOS 2012

101002 Analysis

Schlagwörter

ASJC Scopus Sachgebiete

Nuclear and High Energy Physics, Statistical and Nonlinear Physics, Mathematical Physics

Link zum Portal

https://ucrisportal.univie.ac.at/de/publications/33aedcb8-ce5f-4c11-b915-805bac1e85ee