arXiv subjects

Surena Hozoori

Publications and source records attributed to Surena Hozoori.

7 recordsLinked to original sources

arXiv2026

Anosov contact metrics, Dirichlet optimization and entropy

The first main result of this paper classifies contact 3-manifolds admitting critical metrics, i.e. adapted metrics which are the critical points of the Dirichlet energy functional. This gives a complete answer to a question raised by Chern-Hamilton in 1984. Secondly, we show that in the case of Anosov contact metrics, the optimization of such energy functional is closely related to Reeb dynamics and can be described in terms of its entropy. We also study the consequences in the curvature realization problem for such contact metrics.

math.DG↗

arXiv2025

Strongly adapted contact geometry of Anosov 3-flows

We provide a 3 dimensional contact geometric characterization of Anosov 3-flows based on interactions with Reeb dynamics. We investigate basic properties of the space of the resulting geometries and in particular show that such space is homotopy equivalent to the space of Anosov 3-flows. A technical theorem on the asymptotic synchronization of adapted norms is proved, which can be of broader interest.

math.SG↗

arXiv2024

Regularity and persistence in non-Weinstein Liouville geometry via hyperbolic dynamics

We explore the construction of non-Weinstein Liouville geometric objects based on Anosov 3-flows, intoduced by Mitsumatsu, in the generalized framework of Liouville Interpolation Systems and non-singular partially hyperbolic flows. We study the subtle phenomena inherited from the regularity and persistence theory of hyperbolic dynamics in the resulting Liouville structures, and prove dynamical and geometric rigidity results in this context. Among other things, we show that Mitsumatsu's examples characterize 4-dimensional non-Weinstein Liouville geometry with 3-dimensional $C^1$-persistent transverse skeleton. We also draw applications to the regularity theory of the weak dominated bundles for non-singular partially hyperbolic 3-flows.

math.DS↗

arXiv2024

Symplectic Geometry of Anosov Flows in Dimension 3 and Bi-Contact Topology

We give a purely contact and symplectic geometric characterization of Anosov flows in dimension 3 and discuss a framework to use tools from contact and symplectic geometry and topology in the study of Anosov dynamics. We also discuss some uniqueness results regarding the underlying (bi)-contact structures for an Anosov flow and give a characterization of Anosovity based on Reeb flows.

math.SG↗

arXiv2022

On Anosovity, divergence and bi-contact surgery

We discuss a metric description of the divergence of a (projectively) Anosov flow in dimension 3, in terms of its associated growth rates and give metric and contact geometric characterizations of when a projectively Anosov flow is Anosov. Then, we study the symmetries that the existence of an invariant volume form yields on the geometry of an Anosov flow, from various viewpoints of the theory of contact hyperbolas, Reeb dynamics and Liouville geometry, and give characterizations of when an Anosov flow is volume preserving in terms of those theories. We finally use our study to show that the bi-contact surgery operations of Salmoiraghi can be applied in an arbitrary small neighborhood of a periodic orbit of any Anosov flow. In particular, we conclude that the Goodman surgery of Anosov flows can be performed using a bi-contact surgery of Salmoiraghi.

math.DS↗

arXiv2019

Ricci Curvature, Reeb Flows and Contact 3-Manifolds

Given a contact 3-manifold we consider the problem of when a given function can be realized as the Ricci curvature of a Reeb vector field for the contact structure. We will use topological tools to show that every admissible function can be realized as such Ricci curvature for a singular metric which is an honest compatible metric away from a measure zero set. However, we will see that resolving such singularities depends on contact topological data and is yet to be fully understood.

math.DG↗

arXiv2019

Dynamics and Topology of Conformally Anosov Contact 3-Manifolds

We provide obstructions to the existence of conformally Anosov Reeb flows on a 3-manifold that partially generalize similar obstructions to Anosov Reeb flows. In particular, we show $\mathbb{S}^3$ does not admit conformally Anosov Reeb flows. We also give a Riemannian geometric condition on a metric compatible with a contact structure implying that a Reeb field is Anosov. From this we can give curvature conditions on a metric compatible with a contact structure that implies universal tightness of the contact structure among other things.

math.GT↗