Year: 2026
Type: preprint
Abstract: For each $n\geq 4$, we show that the infimal Willmore energy of a non-orientable surface of odd genus immersed in $\mathbb{S}^n$ is attained by an index $(n+1)$ minimal surface in this class. For $n=4$, we obtain in addition the analogous conclusion for surfaces with non-zero Euler number. The proof uses the fact that such surfaces represent a non-trivial cobordism class together with an observation of M. Gromov relating the conformal area in $\mathbb{S}^n$ to minimal fillings in the hyperbolic space $\mathbb{H}^{n+1}$.
Source: arXiv (Cornell University)
Authors: Bernstein, Jacob, Ketover, Daniel
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223005834