Dorian Martino

collaborators

8 papers

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.DG2025

Weak immersions with second fundamental form in a critical Sobolev space

Dorian Martino, Tristan RiviÃ¨re

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 RiviÃ¨re

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…

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

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