Research

(Reviews of papers: Here or here.)

Papers:

• Classical equivalence and quantum equivalence of magnetic fields on flat tori. (dvi) (pdf) With C.S. Gordon, W. Kirwin, and D. Webb. http://arxiv.org/abs/1108.5113. To appear in: Spectral Geometry (Hanover, NH, 2010), Amer. Math. Soc. (Proc. Symp. Pure Math.)
• Local symmetry of harmonic spaces as determined by the spectra of small geodesic spheres. (dvi) (pdf) With T. Arias-Marco. Geom. Funct. Analysis (GAFA) 22 (2012), no. 1, 1-21.

• Quantum equivalent magnetic fields that are not classically equivalent. (dvi) (pdf) With C.S. Gordon, W. Kirwin, and D. Webb. Ann. Inst. Fourier 60 (2010), no. 7, 2403-2419.
• On inaudible curvature properties of closed Riemannian manifolds. (dvi) (pdf) With T. Arias-Marco. Ann. Glob. Anal. Geom. 37 (2010), no. 4, 339-349.
• Spectral isolation of bi-invariant metrics on compact Lie-groups. (dvi) (pdf) With C.S. Gordon and C.J. Sutton. Ann. Inst. Fourier 60 (2010), no. 5, 1617-1628.
• Isospectral orbifolds with different maximal isotropy orders. (ps) (pdf) With J.P. Rossetti and M. Weilandt. Ann. Glob. Anal. Geom. 34 (2008), no. 4, 351-366.
• Integrability of geodesic flows and isospectrality of Riemannian manifolds. (dvi) (pdf) Math. Z. 260 (2008), no. 3, 595-613.
• Isoscattering deformations for complete manifolds of negative curvature. (dvi) (pdf) With P. Perry. J. Geom. Analysis 16 (2006), no. 4, 661-677.
• Isospectral and isoscattering manifolds: A survey of techniques and examples. (dvi) (pdf) With C. Gordon and P. Perry. In: Geometry, spectral theory, groups, and dynamics (M. Entov, Y. Pinchover, M. Sageev, eds.), Contemp. Math. 387 (2005), 157-179.
• On the 'standard' condition for noncompact homogeneous Einstein spaces. (dvi) (pdf) Geom. Dedicata 105 (2004), no. 1, 77-83.
• Isospectral potentials and conformally equivalent isospectral metrics on spheres, balls and Lie groups. (dvi) (pdf) With C.S. Gordon. J. Geom. Analysis 13 (2003), no. 2, 300-328.
• Constructing isospectral metrics via principal connections. (dvi) (pdf), in: Geometric Analysis and Nonlinear Partial Differential Equations (S. Hildebrandt, H. Karcher eds.), Springer, 2003, pp. 69-79.
• Isospectral metrics on five-dimensional spheres. (dvi) (pdf) J. Differential Geometry 58 (2001), 87-111.
• Isospectral manifolds with different local geometries (Habilitationsschrift, Bonn 2000). (dvi) (pdf) Journal für die Reine und Angewandte Mathematik (Crelle), 534 (2001), 41-94.
• Continuous families of isospectral metrics on simply connected manifolds. (dvi) (pdf) Annals of Mathematics 149 (1999), 287-308 (... and some publicity).
• Isospectral deformations of closed Riemannian with different scalar curvature. With C. Gordon, R. Gornet, D. Webb, and E. Wilson. Ann. Inst. Fourier 48 (1998), no. 2, 593-607.
• Symplectic rigidity of geodesic flows on two-step nilmanifolds. With C. Gordon and Y. Mao. Ann. Sci. Ecole Norm. Sup. (4) 30 (1997), no. 4, 417-427.
• Line bundle Laplacians over isospectral nilmanifolds. Trans. Amer. Math. Soc. 349 (1997), no. 9, 3787-3802.
• Distinguishing isospectral nilmanifolds by bundle Laplacians. With C. Gordon and H. Ouyang. Math. Res. Letters 4 (1997), no. 1, 23-33.
• Continuous families of quasi-regular representations on solvable Lie groups. J. Funct. Analysis 134 (1995), no. 1, 247-259.
• Isospectral deformations on Riemannian manifolds which are diffeomorphic to compact Heisenberg manifolds. Comment. Math. Helvetici 70 (1995), 434-454.
• Isospectral, non-isometric Riemannian manifolds. Proceedings of the 13th Winter School on Geometry and Physics (Zdikov 1993). Suppl. Rend. Circ. Mat. Palermo 37 (1994), 207-231.
• Stetige isospektrale Deformationen. Dissertation (Bonn, 1993), Bonner Math. Schriften 261 (1994).
• A new example of an isospectrally deformable solvmanifold and the geometry of the deformation. Rencontres de Théorie Spectrale et Géométrie (Aussois, 1991), 129-131, Univ. Grenoble I, St. Martin d'Hères.