Related papers: Zero entropy on entire Grauert tubes

In this article, we study the ergodicity of the geodesic flows on surfaces with no focal points. Let $M$ be a smooth connected and closed surface equipped with a $C^\infty$ Riemannian metric $g$, whose genus $\mathfrak{g} \geq 2$. Suppose…

Assisted by general symmetry arguments and a many-body invariant, we introduce a phase of matter that constitutes a topological SO(5) superfluid. Key to this finding is the realization of an exactly solvable model that displays some…

For bi-Lipschitz homeomorphisms of a compact manifold it is known that topological entropy is always finite. For compact manifolds of dimension two or greater, we show that in the closure of the space of bi-Lipschitz homeomorphisms, with…

Let $M_{\tau_0}$ be the Grauert tube (of some fixed radius $\tau_0$) of a compact, negatively curved, real analytic Riemannian manifold $M$ without boundary. Let $\phi_\lambda$ be a Laplacian eigenfunction on $M$ of eigenvalues $-\lambda^2$…

We define the class of high dimensional graph manifolds. These are compact smooth manifolds supporting a decomposition into finitely many pieces, each of which is diffeomorphic to the product of a torus with a finite volume hyperbolic…

In this article, we give explicit examples of infinitely many non-commensurable (non-arithmetic) hyperbolic $3$-manifolds admitting exactly $k$ totally geodesic surfaces for any positive integer $k$, answering a question of Bader, Fisher,…

We define a hierarchy of systems with topological completely positive entropy in the context of continuous countable amenable group actions on compact metric spaces. For each countable ordinal we construct a dynamical system on the…

We prove that for every closed, connected, orientable, irreducible 3-manifold, there exists an alternating group A_n which is not the topological symmetry group of any graph embedded in the manifold. We also show that for every finite group…

It is classically known that complete flat surfaces in Euclidean 3-space are cylinders over space curves. This implies that the study of global behaviour of flat surfaces requires the study of singular points as well. If a flat surface $f$…

Both the gauge groups and $5$-manifolds are important in physics and mathematics. In this paper, we combine them together to study the homotopy aspects of gauge groups over $5$-manifolds. For principal bundles over non-simply connected…

We show that many 3-manifold groups have no nonabelian surface subgroups. For example, any link of an isolated complex surface singularity has this property. In fact, we determine the exact class of closed graph-manifolds which have no…

In this paper we consider on a complete Riemannian manifold $M$ an immersed totally geodesic hypersurface $\Si$ existing together with an immersed submanifold $N$ without focal points. No curvature condition is needed. We obtained several…

Under mild assumptions on a group G, we prove that the class of complete Riemannian n-manifolds of uniformly bounded negative sectional curvatures and with the fundamental groups isomorphic to G breaks into finitely many tangential homotopy…

An example of a real-analytic metric on a compact manifold whose geodesic flow is Liouville integrable by $C^\infty$ functions and has positive topological entropy is constructed.

The geometric approach to optimal transport and information theory has triggered the interpretation of probability densities as an infinite-dimensional Riemannian manifold. The most studied Riemannian structures are Otto's metric, yielding…

Co-compact entropy is introduced as an invariant of topological conjugation for perfect mappings defined on any Hausdorff space(compactness and metrizability not necessarily required). This is achieved through the consideration of…

In this paper, we study the regularity of topological entropy, as a function on the space of Riemannian metrics endowed with the $C^0$ topology. We establish several instances of entropy robustness (persistence of entropy non-vanishing…

We prove that the topological entropy of any dominant rational self-map of a projective variety defined over a complete non-Archimedean field is bounded from above by the maximum of its dynamical degrees, thereby extending a theorem of…

Interest in Riemannian manifolds with holonomy equal to the exceptional Lie group $\mathrm{G}_2$ have spurred extensive research in geometric flows of $\mathrm{G}_2$-structures defined on seven-dimensional manifolds in recent years. Among…

We study the influence of the existence of totally geodesic null hypersurface on the properties of a Lorentzian manifold. By coupling the rigging technique with the existence of a null foliation we prove the existence of a Riemann flow…