ICTS:32632

Index estimates for constant mean curvature surfaces in 3-manifolds

(2025). Index estimates for constant mean curvature surfaces in 3-manifolds. SciVideos. https://scivideos.org/index.php/icts-tifr/32632

Index estimates for constant mean curvature surfaces in 3-manifolds. SciVideos, Aug. 25, 2025, https://scivideos.org/index.php/icts-tifr/32632 

          @misc{ scivideos_ICTS:32632,
            doi = {},
            url = {https://scivideos.org/index.php/icts-tifr/32632},
            author = {},
            keywords = {},
            language = {en},
            title = {Index estimates for constant mean curvature surfaces in 3-manifolds},
            publisher = {},
            year = {2025},
            month = {aug},
            note = {ICTS:32632 see, \url{https://scivideos.org/index.php/icts-tifr/32632}}
          }
Ben Sharp
Talk numberICTS:32632
Source RepositoryICTS-TIFR

Abstract

CMC (constant mean curvature) surfaces are critical with respect to area as long as we restrict to competitor surfaces which 'enclose the same volume'. The index of a CMC surface is the number of ways we can locally deform it to reduce its area whilst enclosing the same amount of volume. We will show that the index of a CMC surface is bounded linearly from above in terms of its genus and a Willmore-type energy i.e. the more unstable a surface is the more genus and/or ‘Willmore energy’ it must have. Joint work with Luca Seemungal.