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11.
In this article, we prove existence and uniqueness results for solutions to the outer oblique boundary problem for the Poisson equation under very weak assumptions on boundary, coefficients, and inhomogeneities. The main tools are the Kelvin transformation and the solution operator for the regular inner problem, provided in Grothaus and Raskop (Stochastics 2006; 78(4):233–257). Moreover we prove regularization results for the weak solutions of both the inner and the outer problem. We investigate the nonadmissible direction for the oblique vector field, state results with stochastic inhomogeneities, and provide a Ritz–Galerkin approximation. The results are applicable to problems from Geomathematics (see, e.g., Freeden and Maier (Electronic Trans. Numer. Anal. 2002; 14:40–62 and Bauer, An Alternative Approach to the Oblique Derivative Problem in Potential Theory, Shaker Verlag, Aachen, 2004)). 相似文献
12.
Finite Type Non—Minimal Submanifolds 总被引:1,自引:1,他引:0
The notion of finite type xubmanifolds was introduced by B.Y.Chen.In this paper we consider the characteristics and the classifications of finite type non-minimal submanifolds.The characteristic theorems of 2-type Chen submanifolds、mass-symmetric hypersurfaces and Dupin hypersurfaces in Es^m are obtained.The classification theorems of 3-type hypersurfaces and null 2-type curves in Es^m are also proved. 相似文献
13.
Yingbo Han 《Journal of Mathematical Analysis and Applications》2018,457(1):991-1006
In this paper, we first show that δ-super stable complete noncompact minimal submanifolds in or with admit no nontrivial harmonic 1-forms and have only one nonparabolic end, which generalizes Cao–Shen–Zhu's result in [2] on stable minimal hypersurface in and Lin's result in [13] on -super stable minimal submanifolds in . Second, we prove that the dimension of the space of harmonic p-forms on is zero or finite and there is only one nonparabolic end or finitely many nonparabolic ends of M under the assumptions on the Schrödinger operators involving the squared norm of the traceless second fundamental form. 相似文献
14.
研究了球面Sn+p(c)子流形Mn的Pinching定理,证明了当s<2√n-1c时,Mn(n>3)与n维球面同胚. 相似文献
15.
Recently, Pipoli and Sinestrari [Pipoli, G. and Sinestrari, C., Mean curvature flow of pinched submanifolds of CPn, Comm. Anal. Geom., 25, 2017, 799–846] initiated the study of convergence problem for the mean curvature flow of small codimension in the complex projective space CPm. The purpose of this paper is to develop the work due to Pipoli and Sinestrari, and verify a new convergence theorem for the mean curvature flow of arbitrary codimension in the complex projective space. Namely, the authors prove that if the initial submanifold in CPm satisfies a suitable pinching condition, then the mean curvature flow converges to a round point in finite time, or converges to a totally geodesic submanifold as t → ∞. Consequently, they obtain a differentiable sphere theorem for submanifolds in the complex projective space. 相似文献
16.
The notion of finite type submanifolds was introduced by B.Y.Chen.In this paper the con-jectures on scalar curvature of Veronses generating submanifolds in E^6 and the minimal conjecture on Veronese space-like submanifold ∑ and Veronese pseudo-Riemannian submanifold-↑∑ in E1^6 are proved.We have ∑ is minimal in H^5.-↑∑ is minimal in S1^5,∑ and -↑∑ are of 1-type in E1^6. 相似文献