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Continuity of the renormalised volume between Epstein surfaces with respect to the Weil--Petersson topology
Dorian Martino
We prove that the renormalised volume between the two Epstein surfaces generated by a Weil--Petersson quasicircle is continuous with respect to the Weil--Petersson topology. As a c…
Weak immersions with second fundamental form in a critical Sobolev space
Dorian Martino, Tristan Rivière
We develop the analysis of Lipschitz immersions of -dimensional manifolds into having their second fundamental forms bounded in the critical Sobolev space $W^{\fr…
Construction of harmonic coordinates for weak immersions
Dorian Martino, Tristan Rivière
We prove that any weak immersion in the critical Sobolev space in even dimension , has global harmonic coordinates if its…
A duality theorem for a four dimensional Willmore energy
Dorian Martino
We prove an analog of Bryant's duality theorem for a four dimensional Willmore energy obtained by Graham-Reichert and Zhang. We show that for an immersion fr…
Energy quantization for Willmore surfaces with bounded index
Dorian Martino
We prove an energy quantization result for Willmore surfaces with bounded index, whether the underlying Riemann surfaces degenerates in the moduli space or not. To do so, we transl…
Classification of branched Willmore spheres
Dorian Martino
Given a branched Willmore immersion from a closed Riemann surface, we show that Bryant's quartic is holomorphic. Consequently, this quartic vanishes when the underlying surface is…