A classical result of Milman roughly states that every Lipschitz function on Sn is almost constant on a sufficiently high-dimensional sphere Sm⊂Sn. In this paper we extend the result by proving that any Lipschitz function on a positively curved homogeneous space is almost constant on a high dimensional submanifold.
De Ponti, N. (2022). Concentration on submanifolds of positively curved homogeneous spaces. DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS, 80(February 2022) [10.1016/J.DIFGEO.2021.101847].
Concentration on submanifolds of positively curved homogeneous spaces
De Ponti, N
2022
Abstract
A classical result of Milman roughly states that every Lipschitz function on Sn is almost constant on a sufficiently high-dimensional sphere Sm⊂Sn. In this paper we extend the result by proving that any Lipschitz function on a positively curved homogeneous space is almost constant on a high dimensional submanifold.
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