Displaying similar documents to “Some nonexistence theorems on stable minimal submanifolds”

Willmore submanifolds in the unit sphere.

Guo Zhen (2004)

Collectanea Mathematica

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In this paper we generalize the self-adjoint differential operator (used by Cheng-Yau) on hypersurfaces of a constant curvature manifold to general submanifolds. The generalized operator is no longer self-adjoint. However we present its adjoint operator. By using this operator we get the pinching theorem on Willmore submanifolds which is analogous to the pinching theorem on minimal submanifold of a sphere given by Simon and Chern-Do Carmo-Kobayashi.

Special Lagrangian submanifolds in the complex sphere

Henri Anciaux (2007)

Annales de la faculté des sciences de Toulouse Mathématiques

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We construct a family of Lagrangian submanifolds in the complex sphere which are foliated by ( n - 1 ) -dimensional spheres. Among them we find those which are special Lagrangian with respect to the Calabi-Yau structure induced by the Stenzel metric.

Complete minimal surfaces in ℝ 3 with type Enneper end

Nedir Do Espirito Santo (1994)

Annales de l'institut Fourier

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We show that there exists a complete minimal surface immersed into ℝ 3 which is conformally equivalent to a compact hyperelliptic Riemann surface of genus three minus one point. The end of the surface is of Enneper type and its total curvature is - 16 π .