Related papers: An explicit Enriques surface with an automorphism …

We show the flexibility of the metric entropy and obtain additional restrictions on the topological entropy of geodesic flow on closed surfaces of negative Euler characteristic with smooth non-positively curved Riemannian metrics with fixed…

We present a method for computing the topological entropy of one-dimensional maps. As an approximation scheme, the algorithm converges rapidly and provides both upper and lower bounds.

Let $f$ be an automorphism of a complex Enriques surface $Y$ and let $p_f$ denote the characteristic polynomial of the isometry $f^*$ of the numerical N\'eron-Severi lattice of $Y$ induced by $f$. We apply a modification of McMullen's…

Throughout this paper, we work over ${\mathbb C}$, and $n$ is an integer such that $n\geq 2$. For an Enriques surface $E$, let $E^{[n]}$ be the Hilbert scheme of $n$ points of $E$. By Oguiso and Schr\"oer, $E^{[n]}$ has a Calabi-Yau…

Entropy is a natural geometric quantity measuring the complexity of a surface embedded in $\mathbb{R}^3$. For dynamical reasons relating to mean curvature flow, Colding-Ilmanen-Minicozzi-White conjectured that the entropy of any closed…

We derive a characterization of the complex projective K3 surfaces which have automorphisms of positive entropy in term of their N\'eron-Severi lattices. Along the way, we classify the projective K3 surfaces of zero entropy with infinite…

We characterize Salem numbers which have some power arising as dynamical degree of an automorphism on a complex (projective) 2-Torus, K3 or Enriques surface.

The Ryu-Takayanagi prescription reduces the problem of calculating entanglement entropy in CFTs to the determination of minimal surfaces in a dual anti-de Sitter geometry. For 3D gravity theories and BTZ black holes, we identify the minimal…

We suggest a finite element method for computing minimal surfaces based on computing a discrete Laplace-Beltrami operator operating on the coordinates of the surface. The surface is a discrete representation of the zero level set of a…

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…

We give a "limit-free formula" simplifying the computation of the topological entropy for topological automorphisms of totally disconnected locally compact groups. This result allows us to extend several basic properties of the topological…

For two-dimensional complex tori, we characterize the set of all values of positive entropy that arise from automorphisms. For K3 surfaces, we give suffcient conditions for a positive value to be the entropy of some automorphism.

Triple periodic minimal surfaces (TPMS) have garnered significant interest due to their structural efficiency and controllable geometry, making them suitable for a wide range of applications. This paper investigates the relationships…

We give a complete description of all classical Enriques surfaces with non-zero global vector fields. In particular we show that there are such surfaces. The obtained result also applies to supersingular Enriques surfaces fulfilling a…

This paper develops new tools for understanding surfaces with more than one end (and usually, of infinite topology) which properly minimally embed into Euclidean three-space. On such a surface, the set of ends forms a compact Hausdorff…

In the present paper we describe the K3 surfaces admitting order 11 automorphisms and apply this to classify log Enriques surfaces of global index 11.

We give a method for constructing many examples of automorphisms with positive entropy on rational complex surfaces. The general idea is to begin with a quadratic Cremona transformation that fixes a reduced cubic curve and then use the…

We point out an interesting relation between hypersurface elliptic singularities and log Enriques surfaces: with a few exceptions, every hypersurface elliptic singularity define some klt log Enriques surface $(S,Diff)$. In many cases, the…

Let (M,g) be a compact Riemannian manifold of hyperbolic type, i.e M is a manifold admitting another metric of strictly negative curvature. In this paper we study the geodesic flow restricted to the set of geodesics which are minimal on the…

Let $V$ be a $6$-dimensional complex vector space with an involution $\sigma$ of trace $0$, and let $W \subset \Sym^2 V^\vee$ be a generic $3$-dimensional subspace of $\sigma$-invariant quadratic forms. To these data we can associate an…