On the boundary behavior of mass-minimizing integral currents / Camillo De Lellis, Guido De Philippis, Jonas Hirsch, Annalisa Massaccesi.

Format:

Book

Author/Creator:

De Lellis, Camillo, author.

De Philippis, Guido, author.

Hirsch, Jonas, author.

Massaccesi, Annalisa, author.

Series:

Memoirs of the American Mathematical Society ; v. 1446.

Memoirs of the American Mathematical Society 0065-9266 number 1446

Language:

English

Subjects (All):

Minimal surfaces.

Calculus of variations.

Geometric measure theory.

Currents (Calculus of variations).

Physical Description:

v, 166 pages : illustrations ; 26 cm

Place of Publication:

Providence, Rhode Island : American Mathematical Society [2023]

Summary:

"Let be a smooth Riemannian manifold, a smooth closed oriented submanifold of codimension higher than and an integral area-minimizing current in which bounds . We prove that the set of regular points of at the boundary is dense in . Prior to our theorem the existence of any regular point was not known, except for some special choice of and . As a corollary of our theorem: we answer to a question in Almgren's Almgren's big regularity paper from 2000 showing that, if is connected, then has at least one point of multiplicity , namely there is a neighborhood of the point where is a classical submanifold with boundary ; we generalize Almgren's connectivity theorem showing that the support of is always connected if is connected; we conclude a structural result on when consists of more than one connected component, generalizing a previous theorem proved by Hardt and Simon in 1979 when and is -dimensional." -- Provided by publisher

Contents:

Introduction

Corollaries, open problems, and plan of the paper

Stratification and reduction to collapsed points

Regularity for (Q-1/2) Dir-minimizers

First Lipschitz approximation and harmonic of tangent cones

Decay of the excess and uniqueness of tangent cones

Second Lipschitz approximation

Center manifolds

Monotonicity of the frequency function

Final blow-up argument.

Notes:

"November 2023, volume 291, number 1446 (first of 5 numbers)."

Includes bibliographical references (pages 163-164) and index.

ISBN:

1470466953

9781470466954

OCLC:

1413943828