Every Riemannian manifold diffeomorphic to S^{3} contains at least two distinct embedded minimal 2-spheres.
Ricci flow and contractibility of spaces of metrics
3 Pith papers cite this work. Polarity classification is still indexing.
3
Pith papers citing it
abstract
We show that the space of metrics of positive scalar curvature on any 3-manifold is either empty or contractible. Second, we show that the diffeomorphism group of every 3-dimensional spherical space form deformation retracts to its isometry group. This proves the Generalized Smale Conjecture. Our argument is independent of Hatcher's theorem in the $S^3$ case and in particular it gives a new proof of the $S^3$ case.
fields
math.DG 3representative citing papers
Introduces relative eta invariants for Dirac operators coinciding at infinity on non-compact manifolds with bounded curvature, yielding a spectral flow formula, a new proof of a Gromov-Lawson result, and an APS index theorem generalization to non-compact boundaries.
The moduli space of mean convex two-spheres in complete orientable 3-manifolds with nonnegative Ricci curvature is path-connected; mean convex Heegaard tori have one or two path components depending on a precise characterisation.
citing papers explorer
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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.
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Relative eta invariant and uniformly positive scalar curvature on non-compact manifolds
Introduces relative eta invariants for Dirac operators coinciding at infinity on non-compact manifolds with bounded curvature, yielding a spectral flow formula, a new proof of a Gromov-Lawson result, and an APS index theorem generalization to non-compact boundaries.
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Mean Curvature Flow and Heegaard Surfaces in Lens Spaces
The moduli space of mean convex two-spheres in complete orientable 3-manifolds with nonnegative Ricci curvature is path-connected; mean convex Heegaard tori have one or two path components depending on a precise characterisation.