Attainment of the endpoint degree- infimum

Determine whether the infimum of the energy E_{1/4} over the degree- class A_{-1} is attained at the spectral threshold H=1/4.

Background

The paper proves that the spectral threshold for coercivity is H=1/4 and that the degree- infimum I_{-1}(1/4) is finite and strictly positive. It also constructs degree-zero Weyl sequences whose H2 mass spreads out and whose energy tends to zero, demonstrating loss of compactness at the endpoint.

Although the positive topological energy barrier prevents nonzero-degree configurations from having vanishing energy, the loss of compactness at H=1/4 prevents the existence theory established for H>1/4 from being directly extended to the endpoint. The paper explicitly leaves unresolved whether a degree- minimizer exists at H=1/4.

References

This loss of compactness does not by itself decide whether the endpoint infimum is attained, and the present paper does not address this question.

— Existence and strong-field asymptotics of skyrmions in a fourth-order model of frustrated ferromagnets  (2609.08255 - Li, 8 Sep 2026) in Remark following Theorem threshold, Section 1 (Introduction and main results)