On the geometry of nodal sets and nodal domains

Georgiev, Bogdan

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On the geometry of nodal sets and nodal domains

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Georgiev, Bogdan
Max Planck Institute for Mathematics, Max Planck Society;

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https://hdl.handle.net/20.500.11811/7680
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Citation

Georgiev, B. (2018). On the geometry of nodal sets and nodal domains. PhD Thesis, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn.

Cite as: https://hdl.handle.net/21.11116/0000-0005-1004-4

Abstract

In the present work, we study and prove results related to the nodal geometry of Laplacian eigenfunctions on closed Riemannian manifolds, as well as solutions to more general classes of elliptic partial differential equations. The discussion includes results concerning: nodal set bounds, volumes of tubular neighbourhoods around nodal sets, width and shape of nodal domains, etc.