Exempls of conics arising in two-dimensional Finsler and Lagrange geometries.
Existence of geodesics for the Lorentz metric of a stationary gravitational field
Existence of Holomorphic Functions on Almost Complex Manifolds.
Existence of Metrics With Prescribed Ricci Curvature: Local Theory.
Extended Derdziński-Shen theorem for curvature tensors
We extend a remarkable theorem of Derdziński and Shen, on the restrictions imposed on the Riemann tensor by the existence of a nontrivial Codazzi tensor. We show that the Codazzi equation can be replaced by a more general algebraic condition. The resulting extension applies both to the Riemann tensor and to generalized curvature tensors.
Extremal domains for the first eigenvalue of the Laplace-Beltrami operator
We prove the existence of extremal domains with small prescribed volume for the first eigenvalue of Laplace-Beltrami operator in some Riemannian manifold. These domains are close to geodesic spheres of small radius centered at a nondegenerate critical point of the scalar curvature.