Every Riemannian manifold diffeomorphic to S^{3} contains at least two distinct embedded minimal 2-spheres.
Chun-Pong Chu and Y
2 Pith papers cite this work. Polarity classification is still indexing.
2
Pith papers citing it
abstract
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 proof uses min-max theory, the underlying heuristics are largely inspired by mean curvature flow.
fields
math.DG 2years
2026 2representative citing papers
In 3-spheres with positive Ricci curvature and scalar curvature at least Lambda_0 > 0, there exist four distinct embedded minimal 2-spheres with areas at most 12 pi (i+1)/Lambda_0, plus an application showing at least three non-planar minimal spheres in suitable ellipsoids.
citing papers explorer
-
Existence of two embedded minimal spheres in $S^3$ with an arbitrary metric
Every Riemannian manifold diffeomorphic to S^{3} contains at least two distinct embedded minimal 2-spheres.
-
Minimal spheres and scalar curvature
In 3-spheres with positive Ricci curvature and scalar curvature at least Lambda_0 > 0, there exist four distinct embedded minimal 2-spheres with areas at most 12 pi (i+1)/Lambda_0, plus an application showing at least three non-planar minimal spheres in suitable ellipsoids.