Topological Properties of Neumann Domains
- Author(s)
- Ram Band, David Fajman
- Abstract
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(s)
- Gravitational Physics
- External organisation(s)
- Technion - Israel Institute of Technology
- Journal
- Annales Henri Poincare
- Volume
- 17
- Pages
- 2379–2407
- No. of pages
- 29
- ISSN
- 1424-0637
- DOI
- https://doi.org/10.1007/s00023-016-0468-7
- Publication date
- 09-2015
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101002 Analysis
- Keywords
- ASJC Scopus subject areas
- Nuclear and High Energy Physics, Statistical and Nonlinear Physics, Mathematical Physics
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/topological-properties-of-neumann-domains(33aedcb8-ce5f-4c11-b915-805bac1e85ee).html