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arXiv · 2509.01841

On the properness of $p$-conformal energy on the Teichm\"uller space of a Riemann surface

Hala Alaqad·Jianhua Gong·Gaven Martin·Cong Yao
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Abstract

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 Teichm\"uller space of Riemann surfaces of a fixed genus. This result is an application of a result herein identifying explicitly both the unique extremal mappings of finite distortion between hyperbolic annuli of given modulus, and their $p$-conformal energy.

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Hala Alaqad, Jianhua Gong, Gaven Martin, Cong Yao. 2025-09-01. On the properness of $p$-conformal energy on the Teichm\"uller space of a Riemann surface. https://arxiv.org/abs/2509.01841

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