Minimal submanifolds with $M$-index 2

Minimal Submanifolds

Contents 1. Introduction 2 Part 1. Classical and almost classical results 2 1.1. The Gauss map 3 1.2. Minimal graphs 3 1.3. The maximum principle 5 2. Monotonicity and the mean value inequality 6 3. Rado's theorem 8 4. The theorems of Bernstein and Bers 9 5. Simons inequality 10 6. Heinz's curvature estimate for graphs 10 7. Embedded minimal disks with area bounds 11 8. Stable minimal surfaces ...

Deformations of Minimal Lagrangian Submanifolds with Boundary

Let L be a special Lagrangian submanifold of R with boundary lying on the symplectic, codimension 2 submanifold W . It is shown how deformations of L which keep the boundary of L confined to W can be described by an elliptic boundary value problem, and two results about minimal Lagrangian submanifolds with boundary are derived using this fact. The first is that the space of minimal Lagrangian s...

Complete Embedded Minimal N-submanifolds in C

A classical problem in the theory of minimal submanifolds of Euclidean spaces is to study the existence of a minimal submanifold with a prescribed behavior at infinity, or to determine from the asymptotes the geometry of the whole submanifold. Beyond the intrinsic interest of these questions, they are also of crucial importance when studying the possible singularities of minimal submanifolds in...

Hamiltonian-minimal Submanifolds in Kaehler Manifolds with Symmetries

By making use of the symplectic reduction and the cohomogeneity method, we give a general method for constructing Hamiltonian minimal submanifolds in Kaehler manifolds with symmetries. As applications, we construct infinitely many nontrivial complete Hamiltonian minimal submanifolds in CP n and Cn.

Minimal Lagrangian Submanifolds in Complex Euclidean Space