Equidistribution of minimal hypersurfaces for generic metrics
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Publication:2417970
DOI10.1007/s00222-018-00850-5zbMath1419.53061arXiv1712.06238OpenAlexW2962850487WikidataQ128641912 ScholiaQ128641912MaRDI QIDQ2417970
Antoine Song, André Neves, Fernando Codá Marques
Publication date: 31 May 2019
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1712.06238
Minimal surfaces in differential geometry, surfaces with prescribed mean curvature (53A10) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42) Variational problems concerning minimal surfaces (problems in two independent variables) (58E12)
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Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Morse index and multiplicity of \(\min\text{-}\max\) minimal hypersurfaces
- Raghunathan's topological conjecture and distributions of unipotent flows
- Minimax problems related to cup powers and Steenrod squares
- Dense existence of periodic Reeb orbits and ECH spectral invariants
- Trace formula for compact \(\Gamma \setminus PSL_ 2({\mathbb{R}})\) and the equidistribution theory of closed geodesics
- Isoperimetry of waists and concentration of maps
- Compactness of minimal hypersurfaces with bounded index
- Weyl law for the volume spectrum
- Density of minimal hypersurfaces for generic metrics
- Geodesic planes in hyperbolic 3-manifolds
- Existence of infinitely many minimal hypersurfaces in positive Ricci curvature
- Ergodic theoretic proof of equidistribution of Hecke points
- Seminar on Differential Geometry. (AM-102)
- Regularity of stable minimal hypersurfaces
- On the space of ergodic invariant measures of unipotent flows
- On the bumpy metrics theorem for minimal submanifolds
- An Infinite Dimensional Version of Sard's Theorem
- The Equidistribution of Closed Geodesics
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