Widths of balls and free boundary minimal submanifolds

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...

Widths of l p balls

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 ...

The Gelfand widths of ℓp-balls for 0<p≤1

We provide sharp lower and upper bounds for the Gelfand widths of lp-balls in the N -dimensional lNq -space for 0 < p ≤ 1 and p < q ≤ 2. Such estimates are highly relevant to the novel theory of compressive sensing, and our proofs rely on methods from this area.

Holomorphic vector fields and minimal Lagrangian submanifolds

The purpose of this note is to establish the following theorem: Let N be a Kahler manifold, L be an oriented immersed minimal Lagrangian submanifold of N without boundary and V be a holomorphic vector field in a neighbourhood of L in N . Let div(V ) be the (complex) divergence of V . Then the integral ∫ L div(V ) = 0. Vice versa suppose that N is Kahler-Einstein with non-zero scalar curvature a...