Non-compactness of the space of min-max minimal hyper-surfaces.

  • Nicolau Sarquis (Imperial College London, United Kingdom)
A3 01 (Sophus-Lie room)


We study the space of minimal hyper-surfaces obtained by Almgren-Pitts min-max theory. The approach is by studying index and area bounds for such hyper-surfaces. It was proven by F.C.Marques and A. Neves that positively curved manifolds admit infinitely many embedded minimal hypersurfaces. We are able to show that these are indeed geometrically distinct embeddings.

Katharina Matschke

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