Einstein gravity, Lagrange-Finsler geometry, and nonsymmetric metrics.
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Vacaru, Sergiu I. (2008)
SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]
Mohammed Ben Ayed, Khalil El Mehdi, Mohameden Ould Ahmedou, Filomena Pacella (2005)
Journal of the European Mathematical Society
We consider the Yamabe type family of problems , in , on , where is an annulus-shaped domain of , , which becomes thinner as . We show that for every solution , the energy as well as the Morse index tend to infinity as . This is proved through a fine blow up analysis of appropriate scalings of solutions whose limiting profiles are regular, as well as of singular solutions of some elliptic problem on , a half-space or an infinite strip. Our argument also involves a Liouville type theorem...
Mahmoudi, Fethi (2006)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Gabriel Rivière (2010)
Journées Équations aux dérivées partielles
We study asymptotic properties of eigenfunctions of the Laplacian on compact Riemannian surfaces of Anosov type (for instance negatively curved surfaces). More precisely, we give an answer to a question of Anantharaman and Nonnenmacher [4] by proving that the Kolmogorov-Sinai entropy of a semiclassical measure for the geodesic flow is bounded from below by half of the Ruelle upper bound. (This text has been written for the proceedings of the Journées EDP (Port d’Albret-June, 7-11 2010))
Tadayuki Matsuzawa, Shukichi Tanno (1982)
Compositio Mathematica
Reshetnyak, Yu.G. (2002)
Sibirskij Matematicheskij Zhurnal
Luca Sabatini (2018)
Applications of Mathematics
The free motion of a thin elastic linear membrane is described, in a simplyfied model, by a second order linear homogeneous hyperbolic system of partial differential equations whose spatial part is the Laplace Beltrami operator acting on a Riemannian 2-dimensional manifold with boundary. We adapt the estimates of the spectrum of the Laplacian obtained in the last years by several authors for compact closed Riemannian manifolds. To make so, we use the standard technique of the doubled manifold to...
Tapia, Victor (2009)
Revista Colombiana de Matemáticas
Huisken, Gerhard (1998)
Documenta Mathematica
Chouikha, A.Raouf (2003)
Balkan Journal of Geometry and its Applications (BJGA)
Philippe Bougerol, Laure Elie (1995)
Annales de l'I.H.P. Probabilités et statistiques
Randa Ben Mahmoud, Hichem Chtioui (2011)
Annales de l’institut Fourier
This paper is devoted to the existence of conformal metrics on with prescribed scalar curvature. We extend well known existence criteria due to Bahri-Coron.
Frank Pacard, Pieralberto Sicbaldi (2009)
Annales de l’institut Fourier
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.
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