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Zero-homogeneous and $O(2)$-equivariant critical points of the Oseen-Frank energy with multiple Frank constants

Luc Nguyen

Abstract

We give an existence and classification result for zero-homogeneous and $O(2)$-equivariant critical points of the Oseen-Frank energy with multiple Frank constants. These critical points carry a topological defect of degree one and are minimizing with respect to $O(2)$-equivariant perturbations supported away from the axis of symmetry.

Zero-homogeneous and $O(2)$-equivariant critical points of the Oseen-Frank energy with multiple Frank constants

Abstract

We give an existence and classification result for zero-homogeneous and -equivariant critical points of the Oseen-Frank energy with multiple Frank constants. These critical points carry a topological defect of degree one and are minimizing with respect to -equivariant perturbations supported away from the axis of symmetry.

Paper Structure

This paper contains 8 sections, 96 equations.

Table of Contents

  1. Introduction
  2. Proof
  3. $O(2)$-equivariant maps
  4. Some sets of $O(2)$-equivariant maps with an isolated singularity
  5. Reduced energy for maps with lifting in $X_j(D)$
  6. Zero-homogeneous and $O(2)$-equivariant critical points
  7. Minimality of $\psi_t$ in $X_1(D)$
  8. Proof of the main theorem

Theorems & Definitions (9)

  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • proof : Proof of Theorem \ref{['Thm:Main']}