School of Mathematical Sciences
Monday, April 7, 2014
Schreiber 006, 12:15
Neumann Nodal Domains
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 nodal domains. We define Neumann nodes and Neumann
nodal domains and present their fundamental topological properties.
These in turn allow to discuss some aspects of counting the number of
Neumann nodal domains, giving estimates on their geometry and
connecting them to the 'usual' nodal domains.The talk is based on joint works in progress with David Fajman, Peter Kuchment, Mark Dennis and Alexander Taylor.
Coffee will be served at 12:00 before the lecture
at Schreiber building 006