ICTS:32606

Higher Genus angel Surfaces

(2025). Higher Genus angel Surfaces. SciVideos. https://scivideos.org/index.php/icts-tifr/32606

Higher Genus angel Surfaces. SciVideos, Aug. 20, 2025, https://scivideos.org/index.php/icts-tifr/32606 

          @misc{ scivideos_ICTS:32606,
            doi = {},
            url = {https://scivideos.org/index.php/icts-tifr/32606},
            author = {},
            keywords = {},
            language = {en},
            title = {Higher Genus angel Surfaces},
            publisher = {},
            year = {2025},
            month = {aug},
            note = {ICTS:32606 see, \url{https://scivideos.org/index.php/icts-tifr/32606}}
          }
Rivu Bardhan
Talk numberICTS:32606
Source RepositoryICTS-TIFR

Abstract

We prove the existence of complete minimal surfaces in $\mathbb{R}^3$ of arbitrary genus $p\, >\, 1$ and least absolute curvature with precisely two ends --- one catenoidal and one Enneper-type --- thereby resolving, affirmatively, a conjecture posed by Weber. These surfaces, which are called \emph{Angel surfaces}, generalize the genus-one example constructed earlier by Fujimori and Shoda. We extend the orthodisk method developed by Weber and Wolf, \cite{weber2002teichmuller}, to construct the minimal surfaces. A central idea in our construction is the notion of \emph{partial symmetry}, which enables us to introduce controlled symmetry into the surface. Reference: [Weber and Wolf(2002)] Matthias Weber and Michael Wolf. Teichm¨uller theory and handle addition for minimal surfaces. Annals of mathematics, pages 713–795, 2002.