Isospectral metrics on weighted projective spaces [Elektronische Ressource] / von Martin Weilandt

Isospectral Metrics on Weighted ProjectiveSpacesDISSERTATIONzur Erlangung des akademischen GradesDr. rer. nat.im Fach Mathematikeingereicht an derMathematisch-Naturwissenschaftlichen Fakultät IIHumboldt-Universität zu BerlinvonDipl.-Math. Martin WeilandtPräsident der Humboldt-Universität zu Berlin:Prof. Dr. Dr. h.c. Christoph MarkschiesDekan der Mathematisch-Naturwissenschaftlichen Fakultät II:Prof. Dr. Peter FrenschGutachter:1. Prof. Dr. Dorothee Schüth2. Prof. Dr. Carolyn Gordon3. Prof. Dr. Christian Bäreingereicht am: 6. April 2010Tag der mündlichen Prüfung: 14. Juli 2010AbstractThe Laplace Operator on compact Riemannian manifolds naturally general-izes to compact Riemannian orbifolds and the spectrum of the resulting operatorconsists only of eigenvalues with finite multiplicities. The observation that thespectrum contains information about the geometry of a manifold (and, more gen-erally, an orbifold) gave rise to a whole field of mathematics. It is an open questionof so-called spectral geometry, whether a manifold and a singular orbifold can beisospectral (i.e., have the same spectrum with the same multiplicities of the eigen-values). Given the various obstructions to the existence of such an example forthe known examples of isospectral good orbifolds, this work is an attempt to shedlight on the spectral geometry of bad by giving the first examples ofisospectral Riemannian metrics on bad orbifolds.