G. Martin

activity

20242026

collaborators

6 papers

math.CV2026

$L^{p}$ -Extremal Teichmüller mappings between Riemann surfaces are diffeomorphisms

Gaven Martin, Cong Yao

We consider minimisers in the homotopy class of a homeomorphism $f_{0} : R \to S$ between analytically finite Riemann surfaces with minimal $L^{p}$ - conformal energy \[ \mathsf{E}_p(f:R,S…

math.CV2025

Diffeomorphic solutions of Ahlfors-Hopf equations

Gaven Martin, Cong Yao

Here we advance the study of boundary the value problem for extremal functions of mean distortion and the associated Teichmüller spaces interpolating between the classical examples…

math.CV2025

On the properness of $p$ -conformal energy on the Teichmüller space of a Riemann surface

Hala Alaqad, Jianhua Gong, Gaven Martin +1

We establish that the $p$ -conformal energy, $p \geq 1$ , defined by the $L^{p}$ -norms of the distortion of Sobolev mappings, is a proper functional on the Teichmüller space of Riemann…

math.CV2024

The exponential Teichmüller theory: Ahlfors--Hopf differentials and diffeomorphisms

Gaven Martin, Cong Yao

We consider minimisers of the $p$ -exponential conformal energy for homeomorphisms $f : R \to S$ of finite distortion $\IK(z,f)$ between analytically finite Riemann surfaces in a fixe…

math.GR2024

On Thin Heckoid and Generalised Triangle Groups in $P S L (2, C)$ }

Alex Elzenaar, Gaven Martin, Jeroen Schillewaert

We provide a brief overview of our upcoming work identifying all the thin Heckoid groups in $P S L (2, C)$ . Here we give a complete list of the $55$ thin generalised triangle…

math.CV2024

Bounding deformation spaces of Kleinian groups with two generators

A. Elzenaar, J. Gong, G. J. Martin +1

In this article we provide simple and provable bounds on the size and shape of the locus of discrete subgroups of $\mathsf{PSL}(2,\mathbb{C})\cong \operatorname{Isom}^+(\mathbb{H}^…

Lp-Extremal Teichmüller mappings between Riemann surfaces are diffeomorphisms

Diffeomorphic solutions of Ahlfors-Hopf equations

On the properness of p-conformal energy on the Teichmüller space of a Riemann surface

The exponential Teichmüller theory: Ahlfors--Hopf differentials and diffeomorphisms

On Thin Heckoid and Generalised Triangle Groups in PSL(2,C)}

Bounding deformation spaces of Kleinian groups with two generators

$L^{p}$ -Extremal Teichmüller mappings between Riemann surfaces are diffeomorphisms

On the properness of $p$ -conformal energy on the Teichmüller space of a Riemann surface

On Thin Heckoid and Generalised Triangle Groups in $P S L (2, C)$ }