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Minimal Graphs in n × and n + 1

Ricardo Sà Earp, Eric Toubiana (2010)

Annales de l’institut Fourier

We construct geometric barriers for minimal graphs in n × . We prove the existence and uniqueness of a solution of the vertical minimal equation in the interior of a convex polyhedron in n extending continuously to the interior of each face, taking infinite boundary data on one face and zero boundary value data on the other faces.In n × , we solve the Dirichlet problem for the vertical minimal equation in a C 0 convex domain Ω n taking arbitrarily continuous finite boundary and asymptotic boundary data.We prove...

Minimal submanifolds in 4 with a g.c.K. structure

Marian-Ioan Munteanu (2008)

Czechoslovak Mathematical Journal

In this paper we obtain all invariant, anti-invariant and C R submanifolds in ( 4 , g , J ) endowed with a globally conformal Kähler structure which are minimal and tangent or normal to the Lee vector field of the g.c.K. structure.

Minimal submanifolds in general (α,β)-spaces

Songting Yin, Qun He, Dinghe Xie (2013)

Annales Polonici Mathematici

The volume forms of general (α,β)-metrics are studied. Some equations for minimal submanifolds in general (α,β)-spaces are established by using the normal frame field, and some minimal surfaces in general (α,β)-spaces with special curvature properties are constructed.

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