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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