ICTS:32648

Does the unit sphere minimize the Laplacian eigenvalues under certain curvature constraints?

(2025). Does the unit sphere minimize the Laplacian eigenvalues under certain curvature constraints?. SciVideos. https://scivideos.org/index.php/icts-tifr/32648

Does the unit sphere minimize the Laplacian eigenvalues under certain curvature constraints?. SciVideos, Aug. 18, 2025, https://scivideos.org/index.php/icts-tifr/32648 

          @misc{ scivideos_ICTS:32648,
            doi = {},
            url = {https://scivideos.org/index.php/icts-tifr/32648},
            author = {},
            keywords = {},
            language = {en},
            title = {Does the unit sphere minimize the Laplacian eigenvalues under certain curvature constraints?},
            publisher = {},
            year = {2025},
            month = {aug},
            note = {ICTS:32648 see, \url{https://scivideos.org/index.php/icts-tifr/32648}}
          }
Aditya Tiwari
Talk numberICTS:32648
Source RepositoryICTS-TIFR

Abstract

The unit sphere minimizes the first positive Laplacian eigenvalue among all compact n-dimensional manifolds with Ricci curvature bounded below by n−1, as a consequence of Lichnerowicz's Theorem. This naturally raises a question about the higher Laplacian eigenvalues: Does the unit sphere minimize all the Laplacian eigenvalues? In this talk, we will explore a class of manifolds whose Laplacian eigenvalues are strictly greater than the corresponding eigenvalues of the unit sphere. These examples provide evidence for such a general minimization in dimensions two and three.