Ricci Flow and the Sphere Theorem
By S. Brendle. 2010
148 citations recorded by the source corpus.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/b9b7bc81d5fa400a62a6cca688bc9be19314837d
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Citations in the corpus
- Embedded minimal tori in S3 and the Lawson conjecture (2012, background): “Σ : x 6= y}, which may be unbounded along the diagonal. Using the inequality (12) and Bony’s strict maximum principle for degenerate elliptic equations, we conclude that the set Ω is open (see [4] or [5], Corollary 9.7). Since Ω is open, it follows from Proposition 9 that ∆ΣΨ(¯x) = 0 for each point ”
- Geometric, topological and differentiable rigidity of submanifolds in space forms (2011, background): “During the past sixty years, there are many progresses on sphere theorems for Riemannian manifolds and submanifolds [2, 5, 8, 12, 13, 19].”
- The sphere theorems for manifolds with positive scalar curvature (2011, background): “During the past six decades, there are many progresses on sphere theorems for Riemannian manifolds and submanifolds [3, 6, 8, 11, 38, 39].”
- Rotational symmetry of self-similar solutions to the Ricci flow (2012, unknown): “5 in [2], the metrics γr converge in C ∞ to a smooth metric γ as r → ∞.”
- Ricci flow with surgery on manifolds with positive isotropic curvature (2017, background): “13 in [5] implies that the set of all orthonormal four-frames {e1, e2, e3, e4} satisfying Rg(τ)(e1, e3, e1, e3) + λ (2)Rg(τ)(e1, e4, e1, e4) + μ(2)Rg(τ)(e2, e3, e2, e3) + λ (2)μ(2)Rg(τ)(e2, e4, e2, e4) − 2λμRg(τ)(e1, e2, e3, e4) = 0 is invariant under parallel transport.”
- On Four-Dimensional Anti-self-dual Gradient Ricci Solitons (2011, unknown): “[4]).”