Bernstein type theorems with flat normal bundle

Smoczyk, Knut; Guofang Wang; Xin, Y. L.
May 2006
Calculus of Variations & Partial Differential Equations;May2006, Vol. 26 Issue 1, p57
Academic Journal
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.


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.


Read the Article


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

Try another library?
Sign out of this library

Other Topics