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Existence and regularity of min-max anisotropic minimal hypersurfaces
Guido De Philippis, Antonio De Rosa, Yangyang Li
In any closed smooth Riemannian manifold of dimension at least three, we use the min-max construction to find anisotropic minimal hyper-surfaces with respect to elliptic integrands…
Minimal hypersurfaces for generic metrics in dimension 8
Yangyang Li, Zhihan Wang
We show that in an -dimensional closed Riemmanian manifold with -generic metrics, every minimal hypersurface is smooth and nondegenerate. This confirms a full generic…
Generic Regularity of Minimal Hypersurfaces in Dimension 8
Yangyang Li, Zhihan Wang
In this paper, we show that every -dimensional closed Riemmanian manifold with -generic metrics admits a smooth minimal hypersurface. This generalized previous results…
An Improved Morse Index Bound of Min-Max Minimal Hypersurfaces
Yangyang Li
In this paper, we give an improved Morse index bound of minimal hypersurfaces from Almgren-Pitts min-max construction in any closed Riemannian manifold ), wh…