A homological characterization of foliations consisting of minimal surfaces.
A method of the determination of a geodesic curve on ruled surface with time-like rulings.
A Morse theory for light rays on stably causal lorentzian manifolds
A typical convex surface contains no closed geodesic.
Closed geodesics on surfaces of genus 0
Closed Legendre geodesics in Sasaki manifolds.
Contributions of rational homotopy theory to global problems in geometry
Convergence of Gradient Curves on Hilbert Manifolds.
Curvature estimates and compactness theorems in 3-manifolds for surfaces that are stationary for parametric elliptic functionals.
Der Indexsatz für geschlossene Geodätische.
Diastolic and isoperimetric inequalities on surfaces
We prove a universal inequality between the diastole, defined using a minimax process on the one-cycle space, and the area of closed Riemannian surfaces. Roughly speaking, we show that any closed Riemannian surface can be swept out by a family of multi-loops whose lengths are bounded in terms of the area of the surface. This diastolic inequality, which relies on an upper bound on Cheeger’s constant, yields an effective process to find short closed geodesics on the two-sphere, for instance. We deduce...
Discrete periodic geodesics in a surface.
Erratum: Geometry of the Rolling Ellipsoid
Existence of a closed geodesic on -convex sets
Existence of geodesics for the Lorentz metric of a stationary gravitational field
Geodesics in Asymmetic Metric Spaces
In a recent paper [17] we studied asymmetric metric spaces; in this context we studied the length of paths, introduced the class of run-continuous paths; and noted that there are different definitions of “length spaces” (also known as “path-metric spaces” or “intrinsic spaces”). In this paper we continue the analysis of asymmetric metric spaces.We propose possible definitions of completeness and (local) compactness.We define the geodesics using as admissible paths the class of run-continuous paths.We...
Geodesics in the compactly supported Hamiltonian diffeomorphism group.
Geodesics on product lorentzian manifolds
Geodesics Satisfying General Boundary Conditions
Geometrical decomposition of the free loop space on a manifold with finitely many closed geodesics.