TITLE

Bernstein type theorems with flat normal bundle

AUTHOR(S)
Smoczyk, Knut; Guofang Wang; Xin, Y. L.
PUB. DATE
May 2006
SOURCE
Calculus of Variations & Partial Differential Equations;May2006, Vol. 26 Issue 1, p57
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We prove Bernstein type theorems for minimal n-submanifolds in Rn+p with flat normal bundle. Those are natural generalizations of the corresponding results of Ecker-Huisken and Schoen-Simon-Yau for minimal hypersurfaces.
ACCESSION #
21722680

 

Related Articles

  • Complete foliations of space forms by hypersurfaces. Caminha, A.; Souza, P.; Camargo, F. // Bulletin of the Brazilian Mathematical Society;Sep2010, Vol. 41 Issue 3, p339 

    We study foliations of space forms by complete hypersurfaces, under some mild conditions on its higher order mean curvatures. In particular, in Euclidean space we obtain a Bernstein-type theorem for graphs whose mean and scalar curvature do not change sign but may otherwise be nonconstant. We...

  • SUBMANIFOLDS WITH POINTWISE 1-TYPE GAUSS MAP. Kim, Young Ho // Bulletin of the Transilvania University of Brasov, Series III: M;2008, Vol. 1 Issue 50, p201 

    We introduce the background of the notion of pointwise 1-type Gauss map defined on the submanifolds of a Euclidean space or a pseudo-Euclidean space and the recent results related to it.

  • Compact hypersurfaces in a Euclidean space. Deshmukh, S // Quarterly Journal of Mathematics;Mar1998, Vol. 49 Issue 193, p35 

    Focuses on the compact hypersurfaces of a euclidean space. Absence of Minkowski integrands; Use of the Gauss and Weingarten formulas; Presence of Ricci curvature.

  • Isoperimetric inequalities for minimal submanifolds in Riemannian manifolds: a counterexample in higher codimension. Bangert, Victor; Röttgen, Nena // Calculus of Variations & Partial Differential Equations;Nov2012, Vol. 45 Issue 3/4, p455 

    For compact Riemannian manifolds with convex boundary, B. White proved the following alternative: either there is an isoperimetric inequality for minimal hypersurfaces or there exists a closed minimal hypersurface, possibly with a small singular set. There is the natural question if a similar...

  • The bounds for the squared norm of the second fundamental form of minimal submanifolds of Sn+p. Liu Jiancheng; Zhang Qiuyan // Balkan Journal of Geometry & Its Applications;2007, Vol. 12 Issue 2, p64 

    The aim of this paper is to study some properties of compact minimal submanifold M of the standard Euclidean sphere Sn+p with flat normal connection. We will give a lower bound for the squared form S of the second fundamental form h of M in terms of the gap n - λ1 when S is constant, where...

  • Intrinsic regular submanifolds in Heisenberg groups are differentiable graphs. Arena, Gabriella; Serapioni, Raul // Calculus of Variations & Partial Differential Equations;Aug2009, Vol. 35 Issue 4, p517 

    We characterize intrinsic regular submanifolds in the Heisenberg group as intrinsic differentiable graphs.

  • Complete bounded null curves immersed in $${\mathbb {C}^3}$$ and $${\rm {SL}(2,\mathbb {C})}$$. Martin, Francisco; Umehara, Masaaki; Yamada, Kotaro // Calculus of Variations & Partial Differential Equations;Sep2009, Vol. 36 Issue 1, p119 

    We construct a simply connected complete bounded mean curvature one surface in the hyperbolic 3-space $${\mathcal {H}^3}$$. Such a surface in $${\mathcal {H}^3}$$ can be lifted as a complete bounded null curve in $${\rm {SL}(2,\mathbb {C})}$$. Using a transformation between null curves in...

  • Blow-up examples for the Yamabe problem. Marques, Fernando C. // Calculus of Variations & Partial Differential Equations;Nov2009, Vol. 36 Issue 3, p377 

    It has been conjectured that if solutions to the Yamabe PDE on a smooth Riemannian manifold ( M n, g) blow-up at a point $${p \in M}$$ , then all derivatives of the Weyl tensor W g of g, of order less than or equal to $${[\frac{n-6}{2}]}$$ , vanish at $${p \in M}$$ . In this paper, we will...

  • The Inception of Symplectic Geometry: the Works of Lagrange and Poisson During the Years 1808—1810. Marle, Charles-Michel // Letters in Mathematical Physics;Oct2009, Vol. 90 Issue 1-3, p3 

    We analyse articles by Lagrange and Poisson written two 200 years ago which are the foundation of present-day symplectic and Poisson geometry.

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics