arXiv subjects

Meenakshy Jyothis

Publications and source records attributed to Meenakshy Jyothis.

4 recordsLinked to original sources

arXiv2026

Stars at infinity in the Thurston boundary

We study the stars at infinity in the Thurston boundary of Teichmüller space for the Thurston and Teichmüller metrics. For the Thurston metric, we prove that for every finite-type surface, the star of a projective measured lamination is exactly its zero set, extending a theorem of Liu-Shi from closed surfaces. Moreover, the based star agrees with the star. For the Teichmüller metric, we show that both the based star and the star of a projective measured lamination coincide with its two-step zero set. This set can be strictly larger than the zero set, disproving a conjecture of Karlsson.

math.GT↗

arXiv2026

Geodesic currents of coarse negative curvature

Strong hyperbolicity is a coarse notion of negative curvature, stronger than Gromov hyperbolicity, that includes all CAT(-k) metrics for k positive and allows the use of dynamical techniques available in negative curvature, such as thermodynamical formalism. We prove that the subset of geodesic currents whose dual pseudometric is strongly hyperbolic is dense in the space of geodesic currents. The proof combines an elementary finite-cover argument with a characterization of strong hyperbolicity in terms of boundary data for pseudometrics dual to geodesic currents. In contrast, we show that currents arising from non-positively curved metrics on the surface are not dense. As a consequence, we construct infinitely many pairwise non-roughly-isometric invariant strongly hyperbolic geodesic metrics on the universal cover of the surface which are not CAT(0). Finally, we establish correlation counting results for the associated length spectra.

math.GT↗

arXiv2026

Horoboundary and rigidity of filling geodesic currents

We endow the space of projective filling geodesic currents on a closed hyperbolic surface with a natural asymmetric metric extending Thurston's asymmetric metric on Teichmüller space, as well as analogous metrics arising from Hitchin representations. More generally, we show that this metric extends beyond surface groups and geodesic currents, and encompasses metrics associated with Anosov representations of Gromov hyperbolic groups. We identify the horofunction compactification of the space of projective filling currents equipped with this metric with the space of projective geodesic currents. As a consequence, we obtain a rigidity result: the metric spaces of projective filling geodesic currents associated with closed surfaces of distinct genera are not isometric.

math.GT↗

arXiv2025

Towards Ivanov's meta-conjecture for geodesic currents

Given a closed, orientable surface $S$ of negative Euler characteristic, we study two automorphism groups: $Aut(\mathscr{C})$ and $Aut(\mathcal{ML})$, groups of homeomorphisms that preserve the intersection form in the space $\mathscr{C}$ of geodesic currents and the space $\mathcal{ML}$ of measured laminations. We prove that except in a few special cases, $Aut(\mathcal{ML})$ is isomorphic to the extended mapping class group. This theorem is a special case of \textit{Ivanov's meta-conjecture}. We investigate this question for $Aut(\mathscr{C})$. To demonstrate the difficulty in proving Ivanov's conjecture for $Aut(\mathscr{C})$, we construct infinite family of pairs of closed curves that have the simple same marked length spectra and self intersection number.

math.GT↗