Related papers: Minimal diffeomorphism between hyperbolic surfaces…

In this paper we obtain a bound on the number of isometry classes of finite area hyperbolic surfaces which are length isospectral to a given surface depending only on the topological type of the surface and the length of the shortest closed…

For each integer $g\geq 1$ we use variational methods to construct in the unit $3$-ball $B$ a free boundary minimal surface $\Sigma_g$ of symmetry group $\mathbb{D}_{g+1}$. For $g$ large, $\Sigma_g$ has three boundary components and genus…

For an embedded singly periodic minimal surface M with genus bigger than or equal to 4 and annular ends, some weak symmetry hypotheses imply its congruence with one of the Hoffman-Wohlgemuth examples. We give a very geometrical proof of…

In this article we construct two minimal unique ergodic diffeomorphisms $\alpha$ and $\beta$ on $S^3 \times S^{6} \times S^{8} $. We will show that $C(S^3 \times S^{6} \times S^{8}) \rtimes_\alpha \mathbb{Z} $ and $C(S^3 \times S^{6} \times…

We investigate the existence of minimal hypersurfaces in $\mathbb{S}^{n+1}$ that are generated by the isoparametric foliation of a subsphere $\mathbb{S}^n$. By considering a generalized rotational ansatz formed by the union of homothetic…

We investigate complete minimal submanifolds $f\colon M^3\to\Hy^n$ in hyperbolic space with index of relative nullity at least one at any point. The case when the ambient space is either the Euclidean space or the round sphere was already…

In this paper, we construct infinitely many diffeomorphisms of a Joyce manifold $M$ which achieve Yomdin's homological lower bound for topological entropy, imitating a recent construction of Farb-Looijenga for K3 surfaces. Moreover,…

We prove that all minimal symplectic four-manifolds are essentially irreducible. We also clarify the relationship between holomorphic and symplectic minimality of K\"ahler surfaces. This leads to a new proof of the deformation-invariance of…

First we construct minimal hypersurfaces $M\subset\mathbf{R}^{n+1}$ in a neighborhood of the origin, with an isolated singularity but cylindrical tangent cone $C\times \mathbf{R}$, for any strictly minimizing strictly stable cone $C$ in…

We introduce canonical principal parameters on any strongly regular minimal surface in the three dimensional sphere and prove that any such a surface is determined up to a motion by its normal curvature function satisfying the Sinh-Poisson…

We give a short proof of the following result: Let $X$ be a complex surface of general type. If the canonical divisor of the minimal model of $X$ has selfintersection $= 1$, then $X$ is not diffeomorphic to a rational surface. Our proof is…

We show a $C^r$ connecting lemma for area-preserving surface diffeomorphisms and for periodic Hamiltonian on surfaces. We prove that for a generic $C^r$, $r=1, 2, ...$, $\infty$, area-preserving diffeomorphism on a compact orientable…

Let $ S_g $ be a closed surface of genus $ g $ and let $ (\alpha, \beta) $ be a filling pair on $ S_g $; then $ i(\alpha, \beta) \geq 2g-1 $, where $ i $ is the (geometric) intersection number. Aougab and Huang demonstrated that…

In this article we consider surfaces in the product space $\h^2\times \r$ of the hyperbolic plane $\h^2$ with the real line. The main results are: a description of some geometric properties of minimal graphs; new examples of complete…

We fully characterize the set of finite shapes with minimal perimeter on hyperbolic lattices given by regular tilings of the hyperbolic plane whose tiles are regular $p$-gons meeting at vertices of degree $q$, with $1/p+1/q<\frac{1}{2}$. In…

We consider ``hyperideal'' circle patterns, i.e. patterns of disks appearing in the definition of the Delaunay decomposition associated to a set of disjoint disks, possibly with cone singularities at the center of those disks. Hyperideal…

We explore the relation of weak conjugacy in the group of homeomorphisms isotopic to the identity, for surfaces.

While intersection cohomology is stable under small resolutions, both ordinary and intersection cohomology are unstable under smooth deformation of singularities. For complex projective algebraic hypersurfaces with an isolated singularity,…

The minimal slope conjecture, which was proposed by K.Kedlaya, asserts that two irreducible overconvergent $F$-isocrystals on a smooth variety are isomorphic to each other if both minimal slope constitutions of slope filtrations are…

We prove that the ends of a properly immersed simply or one connected minimal surface in H(2)xR contained in a slab of height less than \pi of H(2)xR, are multi-graphs. When such a surface is embedded then the ends are graphs. When embedded…