SFB 647 I-II: Analytical and Spectral Properties of Geometric Operators (TP B 6)


In project B6 we study relations between analytic properties of geometrically and physically relevant differential operators and the geometry of the underlying manifold. The questions under consideration include analytic properties of operators on singular and possibly incomplete manifolds as well as inverse spectral problems.


Principal Investigators
Schüth, Dorothee Prof. Dr. (Details) (Geometrical Analysis)

Duration of Project
Start date: 01/2005
End date: 12/2016

Publications

C. Gordon, P. Perry, D. Schüth: Isospectral and isoscattering manifolds: A survey of techniques and examples. In: Geometry, spectral theory, groups, and dynamics (M. Entov, Y. Pinchover, M. Sageev, eds.), Contemp. Math. 387 (2005), 157-179.

P. Perry, D. Schüth: Isoscattering deformations for complete manifolds of negative curvature. J. Geom. Analysis, 16(4) (2006), 661-677.

D. Schüth: Integrability of geodesic flows and isospectrality of Riemannian manifolds. Math. Z. 260 (2008), no. 3, 595-613.

J.P. Rossetti, D. Schüth, M. Weilandt: Isospectral orbifolds with different maximal isotropy orders. Ann. Glob. Anal. Geom. 34 (2008), no. 4, 351-366.

C.S. Gordon, D. Schüth, C.J. Sutton: Spectral isolation of bi-invariant metrics on compact Lie groups. Ann. Inst. Fourier 60 (2010), no. 5, 1617-1628.

T. Arias-Marco, D. Schüth: On inaudible curvature properties of closed Riemannian manifolds. Ann. Glob. Anal. Geom. 37 (2010), no. 4, 339-349.

C.S. Gordon, W. Kirwin, D. Schüth, D. Webb: Quantum equivalent magnetic fields that are not classically equivalent. Ann. Inst. Fourier 60 (2010), no. 7, 2403-2419.

T. Arias-Marco, D. Schüth: Local symmetry of harmonic spaces as determined by the spectra of small geodesic spheres. Geom. and Funct. Analysis (GAFA) 22 (2012), no. 1, 1-21.

C.S. Gordon, W. Kirwin, D. Schüth, D. Webb: Classical equivalence and quantum equivalence of magnetic fields on flat tori. Proc. Symp. Pure Math. 84 (2012), 167-179.

T. Arias-Marco, D. Schüth: Inaudibility of sixth order curvature invariants. Rev. R. Acad. Cienc. Exactas, Fis. Nat. 111 (2017), no. 2, 547-574.

D. Schüth: Generic irreducibility of Laplace eigenspaces on certain compact Lie groups. Ann. Glob. Anal. Geom. 52 (2017), no. 2, 187-200.

S. Boldt: Properties of the Dirac spectrum on three dimensional lens spaces. Osaka J. Math. 54 (2017), no. 4, 747-765.

E. Lauret, S. Boldt: An explicit formula for the Dirac multiplicities on lens spaces. J. Geom. Anal. 27 (2017), no. 1, 689–725.

S. Boldt, D. Schüth: Contributions to the spectral geometry of locally homogeneous spaces. Space - time - matter, 69–89, De Gruyter, Berlin, 2018.


Last updated on 2020-20-03 at 23:11