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Topping's diameter conjecture for immersed surfaces

  • Tatsuya Miura
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Abstract

We resolve Topping's diameter conjecture for closed immersed surfaces in Euclidean three-space, building on his recent result for embedded surfaces. More generally, we establish sharp diameter and mean-width estimates for compact connected immersed surfaces, possibly with boundary. As a consequence, we confirm the codimension-one case of the sharp length--diameter conjecture for immersed minimal surfaces.

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Cite

BibTeXRIS
BibTeX
@misc{miura2026toppings,
  title = {{Topping's diameter conjecture for immersed surfaces}},
  author = {Tatsuya Miura},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.01589},
  eprint = {2611.01589},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.01589},
}
RIS
TY  - UNPB
TI  - Topping's diameter conjecture for immersed surfaces
AU  - Tatsuya Miura
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.01589
UR  - https://arxiv.org/abs/2611.01589
AB  - We resolve Topping's diameter conjecture for closed immersed surfaces in Euclidean three-space, building on his recent result for embedded surfaces. More generally, we establish sharp diameter and mean-width estimates for compact connected immersed surfaces, possibly with boundary. As a consequence, we confirm the codimension-one case of the sharp length--diameter conjecture for immersed minimal surfaces.
ER  -