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251.
Alberto Enciso 《Journal of Mathematical Analysis and Applications》2009,354(2):619-624
Let M be a Riemannian manifold such that its geodesic spheres centered at a point a∈M are isoperimetric and the distance function dist(⋅,a) is isoparametric, and let Ω⊂M be a bounded domain. We prove that if there exists a lower bounded nonconstant function u which is p-harmonic (1<p?n) in the punctured domain Ω?{a} such that both u and are constant on ∂Ω, then u is radial and ∂Ω is a geodesic sphere. The proof hinges on a combination of maximum principles, isoparametricity and the isoperimetric inequality. 相似文献
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We give optimal lower bounds for the hypersurface Diracoperator in terms of the Yamabe number, the energy-momentum tensor andthe mean curvature. In the limiting case, we prove that the hypersurfaceis an Einstein manifold with constant mean curvature. 相似文献
254.
Linus Kramer 《Geometriae Dedicata》2000,79(3):321-339
In this third part, we consider those compact quadrangles which arise from isoparametric hypersurfaces of Clifford type and their focal manifolds. Sections 9–11 give a comprehensive introduction to these quadrangles from the incidence-geometric point of view. Section 10 contains also a new (algebraic) proof that these geometries are quadrangles.We determine which of these quadrangles have ovoids or spreads and also whether the normal sphere bundles of the focal manifolds admit sections, or whether they are topologically trivial. We give explicit geometric constructions for spreads, ovoids, and sections. 相似文献
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Let be either a simply connected space form or a rank-one symmetric space of the noncompact type. We consider Weingarten hypersurfaces of , which are those whose principal curvatures and angle function satisfy a relation , being W a differentiable function which is symmetric with respect to . When on the positive cone of , a strictly convex Weingarten hypersurface determined by W is said to be elliptic. We show that, for a certain class of Weingarten functions W, there exist rotational strictly convex Weingarten hypersurfaces of which are either topological spheres or entire graphs over M. We establish a Jellett–Liebmann-type theorem by showing that a compact, connected and elliptic Weingarten hypersurface of either or is a rotational embedded sphere. Other uniqueness results for complete elliptic Weingarten hypersurfaces of these ambient spaces are obtained. We also obtain existence results for constant scalar curvature hypersurfaces of and which are either rotational or invariant by translations (parabolic or hyperbolic). We apply our methods to give new proofs of the main results by Manfio and Tojeiro on the classification of constant sectional curvature hypersurfaces of and . 相似文献
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