ICTS:29933

Video URL

Nash's C^1 isometric embedding theorem and the Borisov-Gromov problem. (RL3)

Nash's C^1 isometric embedding theorem and the Borisov-Gromov problem. (RL3)

(2024). Nash's C^1 isometric embedding theorem and the Borisov-Gromov problem. (RL3). SciVideos. https://youtube.com/live/Fm59kEnMFrk

Nash's C^1 isometric embedding theorem and the Borisov-Gromov problem. (RL3). SciVideos, Sep. 30, 2024, https://youtube.com/live/Fm59kEnMFrk 

          @misc{ scivideos_ICTS:29933,
            doi = {},
            url = {https://youtube.com/live/Fm59kEnMFrk},
            author = {},
            keywords = {},
            language = {en},
            title = {Nash{\textquoteright}s C^1 isometric embedding theorem and the Borisov-Gromov problem. (RL3)},
            publisher = {},
            year = {2024},
            month = {sep},
            note = {ICTS:29933 see, \url{https://scivideos.org/icts-tifr/29933}}
          }
Camillo De Lellis
Talk numberICTS:29933
Source RepositoryICTS-TIFR
Source EventDeterministic and Stochastic Analysis of Euler and Navier-Stokes Equations
Collection

Abstract

In this lecture I will explain the ideas of Nash's surprising construction, in the 1950s, of many C^1 isometric embeddings of Riemannian manifolds as hypersurfaces of the Euclidean space. We will then touch upon an open problem in the area, due to to Borisov and Gromov, about the threshold Hoelder regularity for which the Nash phenomenon is possible. This problem turns out to be intimately linked to the Onsager conjecture and we will survey the results proved so far about it.