46 citations · 110 across the 16 of their papers we have counts for
16 papers
On -manifolds with small mass and -curvature
Conghan Dong, Antoine Song
One of S.T. Yau's problems asks the following: given a -dimensional asymptotically flat manifold with non-negative scalar curvature and -norm of the curvature tensor at…
Entropy and stability of hyperbolic manifolds
Antoine Song
Let be a closed oriented hyperbolic manifold of dimension at least . By the volume entropy inequality of G. Besson, G. Courtois and S. Gallot, for any Riemannian metri…
Stability of Euclidean 3-space for the positive mass theorem
Conghan Dong, Antoine Song
We show that the Euclidean 3-space is stable for the Positive Mass Theorem in the following sense. Let be a sequence of complete asymptotically flat -…
Spherical volume and spherical Plateau problem
Antoine Song
Given a closed oriented manifold or more generally a group homology class, we introduce the spherical Plateau problem, which is a variational problem corresponding to a topological…
On certain quantifications of Gromov's non-squeezing theorem
Kevin Sackel, Antoine Song, Umut Varolgunes +1
Let and let be the Euclidean -ball of radius with a closed subset removed. Suppose that embeds symplectically into the unit cylinder $\mathbb{D}^2 \times…
Essential minimal volume of Einstein 4-manifolds
Antoine Song
The minimal volume of a closed manifold is the infimum of the volume of over all metrics with sectional curvature between and . We introduce a variant calle…
Generic scarring for minimal hypersurfaces along stable hypersurfaces
Antoine Song, Xin Zhou
Let be a closed manifold of dimension . We show that for a -generic metric on , to any connected, closed, embedded, -sided, stable, m…
Morse index, Betti numbers and singular set of bounded area minimal hypersurfaces
Antoine Song
We introduce a combinatorial argument to study closed minimal hypersurfaces of bounded area and high Morse index. Let be a closed Riemannian manifold and …
On the existence of minimal Heegaard surfaces
Daniel Ketover, Yevgeny Liokumovich, Antoine Song
Let be a strongly irreducible Heegaard surface in a closed oriented Riemannian -manifold. We prove that is either isotopic to a minimal surface of index at most one or i…
A dichotomy for minimal hypersurfaces in manifolds thick at infinity
Antoine Song
Let be a complete -dimensional Riemannian manifold with . Our main theorem generalizes the solution of S.-T. Yau's conjecture on the abundance of mini…
Existence of infinitely many minimal hypersurfaces in closed manifolds
Antoine Song
Using min-max theory, we show that in any closed Riemannian manifold of dimension at least 3 and at most 7, there exist infinitely many smoothly embedded closed minimal hypersurfac…
Equidistribution of minimal hypersurfaces for generic metrics
Fernando C. Marques, André Neves, Antoine Song
For almost all Riemannian metrics (in the Baire sense) on a closed manifold , , we prove that there is a sequence of closed, smooth, embedded…
Local min-max surfaces and strongly irreducible minimal Heegaard splittings
Antoine Song
Let be a closed oriented Riemannian -manifold and suppose that there is a strongly irreducible Heegaard splitting . We prove that is either isotopic to a minimal…
Appearance of stable minimal spheres along the Ricci flow in positive scalar curvature
Antoine Song
We construct examples of spherical space forms with positive scalar curvature and containing no stable embedded minimal surfaces, such that the following happens along…
Embeddedness of least area minimal hypersurfaces
Antoine Song
E. Calabi and J. Cao showed that a closed geodesic of least length in a two-sphere with nonnegative curvature is always simple. Using min-max theory, we prove that for some higher…
A maximum principle for self-shrinkers and some consequences
Antoine Song
Using a maximum principle for self-shrinkers of the mean curvature flow, we give new proofs of a rigidity theorem for rotationally symmetric compact self-shrinkers and a result abo…