5 papers
Min-max theory and minimal surfaces with prescribed genus
Adrian Chun-Pong Chu, Yangyang Li, Zhihan Wang
We establish a general min-max type theorem that produces minimal surfaces with prescribed genus in 3-manifolds with positive Ricci curvature. An important intermediate step is to…
An enumerative min-max theorem for minimal surfaces
Adrian Chun-Pong Chu, Yangyang Li, Zhihan Wang
We prove an enumerative min-max theorem that relates the number of genus g minimal surfaces in 3-manifolds of positive Ricci curvature to topological properties of the set of embed…
Strong multiplicity one theorems and homological min-max theory
Adrian Chun-Pong Chu, Yangyang Li
It was asked by Marques-Neves which min-max -widths of the unit -sphere lie strictly between and . We show that the 10th to the 13th widths do. More generally, w…
Existence of 5 minimal tori in 3-spheres of positive Ricci curvature
Adrian Chun-Pong Chu, Yangyang Li
In 1989, B. White conjectured that every Riemannian 3-sphere has at least 5 embedded minimal tori. We confirm this conjecture for 3-spheres of positive Ricci curvature. While our p…
Non-persistence of strongly isolated singularities, and geometric applications
Alessandro Carlotto, Yangyang Li, Zhihan Wang
We obtain a generic regularity result for stationary integral -varifolds with only strongly isolated singularities inside -dimensional Riemannian manifolds, in absence of any…