Dorian Martino

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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, RÃ©my Rodiac

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

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 $I ¨ _{n + k} (N) \neq = {0}$ for some $k \geq 0$ , we establish the existence of nontrivial $n$ -harmonic maps fro…

math.AP2025

A weak energy identity for $(n + I^\pm)$ -harmonic maps with a free boundary in a sphere

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

math.AP2025

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…

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

A weak energy identity for (n+I^±)-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

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 $(n + I^\pm)$ -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