1,721,019 research outputs found
GRADIENT BOUNDS FOR THE POISSON EQUATION ON COMPLETE RIEMANNIAN MANIFOLDS AND LIOUVILLE’S TYPE THEOREMS
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Liouville type theorems for φ-subharmonic functions
No full textIn this paper we presents some Liouville type theorems for solutions of differential inequalities involving the φ-Laplacian. Our results, in particular, improve and generalize known results for the Laplacian and the p-Laplacian, and are new even in these cases. PhragmenLindeloff type results, and a weak form of the Omori-Yau maximum principle are also discussed
Remarks on the geometry of surfaces in the four-dimensional Mobius sphere
No full textWe study the conformal geometry of surfaces immersed in the fourdimensional conformal sphere Q4, viewed as a homogeneous space under the action of the Mobius group. We introduce the classes of isotropic surfaces and characterize them as those whose conformal Gauss map is antiholomorphic or holomorphic. We then relate these surfaces to Willmore surfaces and prove some vanishing results and some bounds on the Euler characteristic of the surfaces. Finally, we characterize isotropic surfaces through an Enneper-Weierstrass-type parametrization.We study the conformal geometry of surfaces immersed in the four-dimensional conformal sphere Q4, viewed as a homogeneous space under the action of the Möbius group. We introduce the classes of ± isotropic surfaces and characterize them as those whose conformal Gauss map is antiholomorphic or holomorphic. We then relate these surfaces to Willmore surfaces and prove some interesting vanishing results and some bounds on the Euler characteristic of the surfaces. Finally, we characterize - isotropic surfaces through an Enneper-Weierstrass-typeparametrization
Positive solutions of Yamabe type equations on complete manifolds and applications
No full textAbstractWe study the semilinear equationΔu+a(x)u=b(x)uσ(σ>1) on a complete Riemannian manifold. We determine conditions on the coefficients that guarantee existence and nonexistence of positive solutions. A very general uniqueness result is also established. Our main results are valid without explicit curvature assumptions, and appear to be new even in Rm
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