2026/08/05 by Haotong Fu, Huaijie Wang, Wei Wang +1
Mathematics · Physics and Astronomy · #math.AP #math-ph #math.DG #math.MP
28 pages, comments are welcome!
arxiv created 2026/08/05 · arxiv updated 2026/08/06
We study local minimizers of a sextic-potential Landau--de Gennes energy for nematic liquid crystals in the small-elastic-constant limit. Under the uniform energy and L^∞ bounds, these minimizers converge to a locally energy-minimizing harmonic map Q0 into a biaxial vacuum manifold. The main result of this paper is that such a limiting map Q0 has no interior point singularities. The proof relies on a geometric identification of the lifted Frobenius metric on the universal cover \mathbbS3 with a rescaled Berger metric. For a hypothetical tangent cone at a point singularity, its link is a nonconstant harmonic two-sphere into the Berger sphere. We construct a smooth variation field adapted to the Hopf direction and show that it induces a quantitative instability estimate, in contradiction with the shifted stability inequality inherited from local minimality. This replaces the usual round-sphere test fields by a target-specific construction and rules out interior point defects in the biaxial setting. The result is sharp in view of the well-known existence of point defects in the uniaxial theory.