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

2025/09/01 by Alaqad, Hala, Gong, Jianhua, Martin, Gaven +1
#30C #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.01841

Abstract

We establish that the p-conformal energy, p≥ 1, defined by the L^p-norms of the distortion of Sobolev mappings, is a proper functional on the Teichmüller 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.

Citations

• The L^p Teichmüller theory: Existence and regularity of critical points
• Harmonic Maps and Teichmueller Theory

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