Skip to content
DraconiticResearch
Search Sources API
203,234 studies31 sourcesUpdated 40 min ago
PreprintarXiv licencearXiv

Willmore energy and minimal fillings

  • Jacob Bernstein
  • Daniel Ketover
Open at sourcePDFDOICite

Abstract

For each nβ‰₯ 4, we show that the infimal Willmore energy of a non-orientable surface of odd genus immersed in π•Šn 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 π•Šn to minimal fillings in the hyperbolic space ℍn+1.

Related

  1. Minimal equatorial fillings of low index
    Jacob Bernstein, Daniel Ketover
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  2. Minimal equatorial fillings
    Jacob Bernstein, Daniel Ketover
    arXivPreprintCC BY 4.0Full textGeometry & topologyarXiv
  3. The Willmore Energy Landscape of Spheres and Avoidable Singularities of the Willmore Flow
    Elena MΓ€der-Baumdicker, Jona Seidel
    Forum of Mathematics, SigmaPeer-reviewedCC BY 4.0Full textGeneral mathematicsCrossref
  4. Eventual Monotonicity of the Willmore Energy under Mean Curvature Flow
    Yuyue Chen, Shiying Wu
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv
  5. On the Willmore energy of flat n-tori in ℝN and Chen's conjecture for n-tori
    Ruijie Ni, Peng Wang, Zhenxiao Xie
    arXivPreprintarXiv licenceFull textGeometry & topologyarXiv

Cite

BibTeXRIS
BibTeX
@misc{bernstein2026willmore,
  title = {{Willmore energy and minimal fillings}},
  author = {Jacob Bernstein and Daniel Ketover},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.26331},
  eprint = {2610.26331},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.26331},
}
RIS
TY  - UNPB
TI  - Willmore energy and minimal fillings
AU  - Jacob Bernstein
AU  - Daniel Ketover
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.26331
UR  - https://arxiv.org/abs/2610.26331
AB  - For each nβ‰₯ 4, we show that the infimal Willmore energy of a non-orientable surface of odd genus immersed in π•Š^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 π•Š^n to minimal fillings in the hyperbolic space ℍ^n+1.
ER  -