相关论文: Any 3-manifold 1-dominates at most finitely many g…

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 hypersurfaces. It proves a conjecture of S.-T. Yau. This paper builds…

In this paper we determined all of the possible self mapping degrees of the manifolds with $S^3$-geometry, which are supposed to be all 3-manifolds with finite fundamental groups. This is a part of a project to determine all possible self…

We show that any collection of n-dimensional orbifolds with sectional curvature and volume uniformly bounded below, diameter bounded above, and with only isolated singular points contains orbifolds of only finitely many orbifold…

We show that a hyperbolic three-manifold $M$ containing a closed minimal surface with principal curvatures in $[-1,1]$ also contains nearby (non-minimal) surfaces with principal curvatures in $(-1,1)$. When $M$ is complete and homeomorphic…

We prove that the fundamental group of any Seifert 3-manifold is conjugacy separable. That is, conjugates may be distinguished in finite quotients or, equivalently, conjugacy classes are closed in the pro-finite topology.

We prove that the set of diffeomorphisms having at most finitely many attractors contains a dense and open subset of the space of $C^1$ partially hyperbolic diffeomorphisms with one-dimensional center. This is obtained thanks to a robust…

In this paper, we show that Gromov-Thurston's principle works for hyperbolic 3-manifolds of infinite volume and with finitely generated fundamental group. As an application, we have a new proof of Ending Lamination Theorem. Our proof…

We show that there exist infinitely many closed 3-manifolds that do not embed in closed symplectic 4-manifolds, disproving a conjecture of Etnyre-Min-Mukherjee. To do this, we construct L-spaces that cannot bound positive or negative…

We show that any compact orientable hyperbolic 3-cone-manifold with cone angle at most \pi can be continuously deformed to a complete hyperbolic manifold homeomorphic to the complement of the singularity. This together with the local…

We prove there exists a compact embedded minimal surface in a complete finite volume hyperbolic $3$-manifold $\mathcal{N}$. We also obtain a least area, incompressible, properly embedded, finite topology, $2$-sided surface. We prove a…

It is shown that for given positive integers g and b, there is a number C(g,b), such that any orientable compact irreducible 3-manifold of Heegaard genus g has at most C(g,b) disjoint, nonparallel incompressible surfaces with first Betti…

We show that in cohomogeneity 3 there are G-manifolds with any given number of isolated singular orbits and an invariant metric of positive Ricci curvature. We show that the corresponding result is also true in cohomogeneity 5 provided the…

This notes explores angle structures on ideally triangulated compact $3$-manifolds with high genus boundary. We show that the existence of angle structures implies the existence of a hyperbolic metric with totally geodesic boundary, and…

It is conjectured that every cusped hyperbolic 3-manifold has a decomposition into positive volume ideal hyperbolic tetrahedra (a "geometric" triangulation of the manifold). Under a mild homology assumption on the manifold we construct…

This paper studies closed 3-manifolds which are the attractors of a system of finitely many affine contractions that tile $\mathbb{R}^3$. Such attractors are called self-affine tiles. Effective characterization and recognition theorems for…

We characterize f-vectors of sufficiently large three-dimensional flag Gorenstein* complexes, essentially confirming a conjecture of Gal [Discrete Comput. Geom., 34 (2), 269--284, 2005]. In particular, this characterizes f-vectors of large…

We characterize the standard $\mathbb{S}^3$ as the closed Ricci-positive 3-manifold with scalar curvature at least 6 having isoperimetric surfaces of largest area: $4\pi$. As a corollary we answer in the affirmative an interesting special…

In this paper it is proven that there is at most one way, up to isotopy, in which a connected, hyperbolic, orientable 3-manifold can fiber over the circle with monodromy in the Torelli group.

We prove an extension of Milnor-Wood inequalities to a geometric situation. We study representations of the fundamental group of a compact manifold into the isometry group of a product of rank one spaces of the same dimension and show an…

We study the large-scale geometry of 3-manifolds with nontrivial 2-dimensional bounded cohomology, with a view to proving a weak version of the geometrization conjecture for such manifolds.