Dorian Martino

activity

20232026

most citedRegularizing properties of n-Laplace systems with antisymmetric potentials in Lorentz spaces

6 citations · 9 across the 15 of their papers we have counts for

collaborators

15 papers

math.DG2026

Comparison between renormalized volume and area in the Weil--Petersson topology

Dorian Martino

We prove that the renormalized volume between the two Epstein surfaces associated with a Weil--Petersson quasicircle is continuous with respect to the Weil--Petersson topology. As…

math.AP2026

Non-Regularizing properties of $n$ -Laplace systems with antisymmetric potentials in critical Lebesgue spaces

Dorian Martino, Armin Schikorra

For every $n \geq 3$ we construct a bounded discontinuous map $u \in W^{1, n} (B^{n}, R^{n + 2})$ solving an $n$ -Laplace system with an antisymmetric potential $Ω \in L^{n}$ .…

math.AP2026

On minimizing $W^{s, 1/ s}$ -maps between circles

Dorian Martino, Katarzyna Mazowiecka, Armin Schikorra

For $s \in (1/4, 1)$ and any degree the only $W^{s, \frac{1}{s}}$ -minimizers for $S^{1} \to S^{1}$ maps are Blaschke products. This gives a resolution of Open Problems…

math.AP2026

Minimizing and non-minimizing degree one $W^{s, 1/ s}$ -harmonic maps between spheres

Dorian Martino, Katarzyna Mazowiecka, Armin Schikorra

We show that $i d : S^{1} \to S^{1}$ is \emph{not} a minimizing $W^{s, \frac{1}{s}}$ -harmonic map for $s \in (0, \frac{1}{8}$ ). On the other hand, for $s \in (\frac{1}{3},…

math.AP2026

Min-max $n$ -harmonic maps of degree 1 with free-boundary into $S^{n - 1}$ in almost round balls

Dorian Martino, Katarzyna Mazowiecka, Rémy Rodiac

Let $n \geq 3$ and let $Ω \subset R^{n}$ be a $C^{1}$ bounded domain which is diffeomorphic to a ball. We investigate here the problem of finding critical points of th…

math.AP2026

Existence of nontrival $n$ -harmonic maps via min-max methods

Dorian Martino, Katarzyna Mazowiecka, Armin Schikorra

For any $n \geq 3$ and any closed manifold $N$ with $π_{n + k} (N) \neq = {0}$ for some $k \geq 0$ , we establish the existence of nontrivial $n$ -harmonic maps from…

math.DG2025

Weak immersions with second fundamental form in a critical Sobolev space

Dorian Martino, Tristan Rivière

We develop the analysis of Lipschitz immersions of $n$ -dimensional manifolds into $R^{d}$ having their second fundamental forms bounded in the critical Sobolev space $W^{\fr…

math.DG2025

Construction of harmonic coordinates for weak immersions

Dorian Martino, Tristan Rivière

We prove that any weak immersion in the critical Sobolev space $W^{\frac{n}{2} + 1, 2} (R^{n}; R^{d})$ in even dimension $n \geq 4$ , has global harmonic coordinates if its…

math.AP2025

A weak energy identity for $(n + α)$ -harmonic maps with a free boundary in a sphere

Dorian Martino, Katarzyna Mazowiecka, Rémy Rodiac

In this article, we show that sequences of $(n + α)$ -harmonic maps with a free boundary in $S^{d - 1}$ , where $α$ is a parameter tending to zero, converge to a bubble tree. For…

math.AP2024

Regularity of unconstrained $p$ -harmonic maps from curved domain and application to critical $p$ -Laplace systems

Dorian Martino

Given $p \geq 2$ and a map $g : B^{n} (0, 1) \to S_{n}^{++}$ , where $S_{n}^{++}$ is the group of positively definite matrices, we study critical points of the following functional: $$ v\in W…

math.AP2024

A note on limiting Calderon-Zygmund theory for transformed $n$ -Laplace systems in divergence form

Dorian Martino, Armin Schikorra

We consider rotated $n$ -Laplace systems on the unit ball $B_{1} \subset R^{n}$ of the form \begin{align*} -\mathrm{div}\left( Q|\nabla u|^{n-2} \nabla u\right) = \mathrm{div}(…

math.DG2023

A duality theorem for a four dimensional Willmore energy

Dorian Martino

We prove an analogue of the energy identities underlying Bryant's duality theorem for a four-dimensional Willmore energy $E_{GR}$ obtained by Graham--Reichert and Zha…

math.DG2023★ 2 cited

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…

math.DG2023★ 1 cited

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…

math.AP2023★ 6 cited

Regularizing properties of n-Laplace systems with antisymmetric potentials in Lorentz spaces

Dorian Martino, Armin Schikorra

We show continuity of solutions $u \in W^{1, n} (B^{n}, R^{N})$ to the system \[ -{\rm div} (|\nabla u|^{n-2} \nabla u) = Ω\cdot |\nabla u|^{n-2} \nabla u \] when $Ω$ is an $L^{n}$ …

Comparison between renormalized volume and area in the Weil--Petersson topology

Non-Regularizing properties of n-Laplace systems with antisymmetric potentials in critical Lebesgue spaces

On minimizing Ws,1/s-maps between circles

Minimizing and non-minimizing degree one Ws,1/s-harmonic maps between spheres

Min-max n-harmonic maps of degree 1 with free-boundary into Sn−1 in almost round balls

Existence of nontrival n-harmonic maps via min-max methods

Weak immersions with second fundamental form in a critical Sobolev space

Construction of harmonic coordinates for weak immersions

A weak energy identity for (n+α)-harmonic maps with a free boundary in a sphere

Regularity of unconstrained p-harmonic maps from curved domain and application to critical p-Laplace systems

A note on limiting Calderon-Zygmund theory for transformed n-Laplace systems in divergence form

A duality theorem for a four dimensional Willmore energy

Energy quantization for Willmore surfaces with bounded index

Classification of branched Willmore spheres

Regularizing properties of n-Laplace systems with antisymmetric potentials in Lorentz spaces

Non-Regularizing properties of $n$ -Laplace systems with antisymmetric potentials in critical Lebesgue spaces

On minimizing $W^{s, 1/ s}$ -maps between circles

Minimizing and non-minimizing degree one $W^{s, 1/ s}$ -harmonic maps between spheres

Min-max $n$ -harmonic maps of degree 1 with free-boundary into $S^{n - 1}$ in almost round balls

Existence of nontrival $n$ -harmonic maps via min-max methods

A weak energy identity for $(n + α)$ -harmonic maps with a free boundary in a sphere

Regularity of unconstrained $p$ -harmonic maps from curved domain and application to critical $p$ -Laplace systems

A note on limiting Calderon-Zygmund theory for transformed $n$ -Laplace systems in divergence form