Antoine Song

activity

20242026

collaborators

5 papers

math.DG2026

On $3$ -manifolds with small mass and $L^{2}$ -curvature

Conghan Dong, Antoine Song

One of S.T. Yau's problems asks the following: given a $3$ -dimensional asymptotically flat manifold $M$ with non-negative scalar curvature and $L^{2}$ -norm of the curvature tensor at…

math.DG2025

On the existence of minimal Heegaard surfaces

Daniel Ketover, Yevgeny Liokumovich, Antoine Song

Let $H$ be a strongly irreducible Heegaard surface in a closed oriented Riemannian $3$ -manifold. We prove that $H$ is either isotopic to a minimal surface of index at most one or i…

math.DG2025

Entropy and stability of hyperbolic manifolds

Antoine Song

Let $(M, g_{0})$ be a closed oriented hyperbolic manifold of dimension at least $3$ . By the volume entropy inequality of G. Besson, G. Courtois and S. Gallot, for any Riemannian metri…

math.DG2025

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…

math.DG2024

Stability of Euclidean 3-space for the positive mass theorem

Conghan Dong, Antoine Song

We show that the Euclidean 3-space $R^{3}$ is stable for the Positive Mass Theorem in the following sense. Let $(M_{i}, g_{i})$ be a sequence of complete asymptotically flat $3$ -…

On 3-manifolds with small mass and L2-curvature

On the existence of minimal Heegaard surfaces

Entropy and stability of hyperbolic manifolds

Spherical volume and spherical Plateau problem

Stability of Euclidean 3-space for the positive mass theorem

On $3$ -manifolds with small mass and $L^{2}$ -curvature