On the Construction of Harmonie and Holomorphic Maps Between Surfaces.
On the continuity of harmonic mappings and the Boundary.
On the curvature of the space of qubits
The Fisher informational metric is unique in some sense (it is the only Markovian monotone distance) in the classical case. A family of Riemannian metrics is called monotone if its members are decreasing under stochastic mappings. These are the metrics to play the role of Fisher metric in the quantum case. Monotone metrics can be labeled by special operator monotone functions, according to Petz's Classification Theorem. The aim of this paper is to present an idea how one can narrow the set of monotone...
On the Differentiable Pinching Problem.
On the differential geometry of frame bundles of Riemannian manifolds.
On the Dirichlet Problem at Infinity for Manifolds of Nonpositive Curvature.
On the Elliptic Equation ...u + K(x)e2u = 0 and Conformal Metrics with Prescribed Gaussian Curvatures..
On the energy of sections of trivializable sphere bundles.
On the energy of unit vector fields with isolated singularities
We consider the energy of a unit vector field defined on a compact Riemannian manifold M except at finitely many points. We obtain an estimate of the energy from below which appears to be sharp when M is a sphere of dimension >3. In this case, the minimum of energy is attained if and only if the vector field is totally geodesic with two singularities situated at two antipodal points (at the 'south and north pole').
On the Ergodicity of Frame Flows.
On the eta invariant, stable positive scalar curvature, and Higher -genera.
On the Existence of Closed Geodesics on Spherical Manifolds.
On the existence of killing tensor fields of type q in a compact Riemannian manifold
On the filling radius of positively curved manifolds.
On the first eigenvalue of the Laplacian for compact submanifolds of Euclidean space.
On the four-dimensional -manifolds of positive Ricci curvature.
On the Fundamental Group of a Visibility Manifold.
On the Fundamental Group of Non-Positively Curved Manifolds.
On the Gauss-Kronecker Curvature Tensors.
On the geodesics flow of tori without conjugate points.