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101.
102.
Vy khoi Le 《Czechoslovak Mathematical Journal》2008,58(2):541-560
The paper is about a sub-supersolution method for the prescribed mean curvature problem. We formulate the problem as a variational
inequality and propose appropriate concepts of sub-and supersolutions for such inequality. Existence and enclosure results
for solutions and extremal solutions between sub-and supersolutions are established. 相似文献
103.
In this paper, we study a second order variational problem for locally convex hypersurfaces, which is the affine invariant analogue of the classical Plateau problem for minimal surfaces. We prove existence, regularity and uniqueness results for hypersurfaces maximizing affine area under appropriate boundary conditions.
104.
J. Carlos Díaz-Ramos Eduardo García-Río Luis Hervella 《Annali di Matematica Pura ed Applicata》2005,184(1):115-130
Total scalar curvatures of geodesic spheres obtained by integrating the second-order scalar invariants of the curvature tensor are investigated. The first terms in their power-series expansions are derived and these results are used to characterize the two-point homogeneous spaces among Riemannian manifolds with adapted holonomy. Dedicated to Professor L. VanheckeMathematics Subject Classification (2000) 53C25, 53C30 相似文献
105.
In this paper we answer to a question raised by Ambrosio and Rigot [L. Ambrosio, S. Rigot, Optimal mass transportation in the Heisenberg group, J. Funct. Anal. 208 (2) (2004) 261-301] proving that any interior point of a Wasserstein geodesic in the Heisenberg group is absolutely continuous if one of the end-points is. Since our proof relies on the validity of the so-called Measure Contraction Property and on the fact that the optimal transport map exists and the Wasserstein geodesic is unique, the absolute continuity of Wasserstein geodesic also holds for Alexandrov spaces with curvature bounded from below. 相似文献
106.
107.
Given a positive function F on S^n which satisfies a convexity condition, we introduce the r-th anisotropic mean curvature Mr for hypersurfaces in R^n+1 which is a generalization of the usual r-th mean curvature Hr. We get integral formulas of Minkowski type for compact hypersurfaces in R^n+1. We give some new characterizations of the Wulff shape by the use of our integral formulas of Minkowski type, in case F=1 which reduces to some well-known results. 相似文献
108.
By variational methods, for a kind of Yamabe problem whose scalar curvature vanishes in the unit ball BN and on the boundary S^N-1 the mean curvature is prescribed, we construct multi-peak solutions whose maxima are located on the boundary as the parameter tends to 0^+ under certain assumptions. We also obtain the asymptotic behaviors of the solutions. 相似文献
109.
In this paper, an adaptive nonmonotone line search method for unconstrained minimization problems is proposed. At every iteration,
the new algorithm selects only one of the two directions: a Newton-type direction and a negative curvature direction, to perform
the line search. The nonmonotone technique is included in the backtracking line search when the Newton-type direction is the
search direction. Furthermore, if the negative curvature direction is the search direction, we increase the steplength under
certain conditions. The global convergence to a stationary point with second-order optimality conditions is established. Some
numerical results which show the efficiency of the new algorithm are reported.
相似文献
110.
We study projective curvature tensor in K-contact and Sasakian manifolds. We prove that (1) if a K-contact manifold is quasi projectively flat then it is Einstein and (2) a K-contact manifold is ξ-projectively flat if and only if it is Einstein Sasakian. Necessary and sufficient conditions for a K-contact manifold to be quasi projectively flat and φ-projectively flat are obtained. We also prove that for a (2n + 1)-dimensional Sasakian manifold the conditions of being quasi projectively flat, φ-projectively flat and locally isometric to the unit sphere S
2n+1 (1) are equivalent. Finally, we prove that a compact φ-projectively flat K-contact manifold with regular contact vector field is a principal S
1-bundle over an almost Kaehler space of constant holomorphic sectional curvature 4. 相似文献