A characterization of revolution quadrics by a system of partial differential equations
- Autores: Vladimir Oliker
- Localización: Proceedings of the American Mathematical Society, ISSN 0002-9939, Vol. 138, Nº 11, 2010, págs. 4075-4080
- Idioma: inglés
- DOI: 10.1090/s0002-9939-2010-10439-2
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Resumen
It is shown that existence of a global solution to a particular nonlinear system of second order partial differential equations on a complete connected Riemannian manifold has topological and geometric implications and that in the domain of positivity of such a solution, its reciprocal is the radial function of only one of the following rotationally symmetric hypersurfaces in : paraboloid, ellipsoid, one sheet of a two-sheeted hyperboloid, and a hyperplane.
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