Some connections between results and problems of De Giorgi, Moser and Bangert

TL;DR

This paper establishes a link between Bangert's rigidity results and De Giorgi's conjecture in phase transitions, focusing on minimal solutions without self-intersections for elliptic integrands of Moser type.

Contribution

It demonstrates a connection between Bangert's theorems and De Giorgi's conjecture, providing new insights into the structure of solutions in elliptic variational problems.

Findings

Proves a rigidity result using Bangert's theorems.

Connects Bangert's question to De Giorgi's conjecture.

Focuses on minimal solutions without self-intersections.

Abstract

Using theorems of Bangert, we prove a rigidity result which shows how a question raised by Bangert for elliptic integrands of Moser type is connected, in the case of minimal solutions without self-intersections, to a famous conjecture of De Giorgi for phase transitions.