The filling radius of homogeneous manifolds
The first eigenvalue of the laplacian on manifolds of non-negative curvature
The fundamental group and the spectrum of the Laplacian.
The fundamental group of compact manifolds without conjugate points.
The Group of Isometries of a Left Invariant Riemannian Metric on a Lie Group.
The heat flows and harmonic maps of complete noncompact Riemannian manifolds.
The inaudible geometry of nilmanifolds.
The Index of Minimal Immersions of S2 into S2n.
The information metric on rational maps.
The ..-invariant of hyperbolic 3-manifolds.
The Isometry Groups of Manifolds of Nonpositive Curvature with Finite Volume.
The isometry groups of riemannian manifolds admitting strictly convex functions
The length spectrum of riemannian two-step nilmanifolds
The Morse landscape of a riemannian disk
We study upper bounds on the length functional along contractions of loops in Riemannian disks of bounded diameter and circumference. By constructing metrics adapted to imbedded trees of increasing complexity, we reduce the nonexistence of such upper bounds to the study of a topological invariant of imbedded finite trees. This invariant is related to the complexity of the binary representation of integers. It is also related to lower bounds on the number of points in level sets of a real-valued...
The Poisson boundary for rank one manifolds and their compact lattices.
The p-spectrum of the Laplacian on compact hyperbolic three manifolds.
The Ruelle rotation of Killing vector fields
We present an explicit formula for the Ruelle rotation of a nonsingular Killing vector field of a closed, oriented, Riemannian 3-manifold, with respect to Riemannian volume.
The Scalar Curvature of Minimal Hypersurfaces in Spheres.
The Schwarz Lemma for nonpositively curved riemannian surfaces.
The Spectrum of the Bochner-Laplace Operator on the 1-Forms on a Compact Riemannian Manifold.