M. Ville

activity

20072025

most citedMilnor numbers for 2-surfaces in 4-manifolds

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

collaborators

17 papers

math.DG2025

Sequences of surfaces in $4$ -manifolds

Marina Ville

Let $(Σ_{n})$ be a sequence of surfaces immersed in a $4$ -manifold $M$ which converges to a branched surface $Σ_{0}$ .\\ We denote by $k_{p}^{T}$ (resp. $k_{p}^{N}$ ) the amount of curvature of…

math.DG2025

Minimal tori in $R^{4}$

Marc Soret, Marina Ville

We describe tools for the study of minimal surfaces in $R^{4}$ ; some are classical (the Gauss maps) and some are newer (the link/braid/writhe at infinity). Then we look for…

math.DG2024

Biharmonic Hypersurfaces in Euclidean Spaces

Hiba Bibi, Marc Soret, Marina Ville

An isometric immersion $X : Σ^{n} ⟶ E^{n + 1}$ is biharmonic if $Δ^{2} X = 0$ , i.e. if $Δ H = 0$ , where $Δ$ and $H$ are the metric Laplacian and the mean curvature ve…

math.GT2022

Random walks and the symplectic representation of the braid group

Marc Soret, Marina Ville

We consider the symplectic representation $ρ_{n}$ of a braid group $B (n)$ in $S p (2 l, Z)$ , for $l = [\frac{n - 1}{2}]$ . If $P$ is a polynomial on the $4 l^{2}$ coefficients…

math.DG2021

Equivalences among parabolicity, comparison principle and capacity on complete Riemannian manifolds

A. Aiolfi, L. Bonorino, J. Ripoll +2

In this work we establish new equivalences for the concept of $p$ -parabolic Riemannian manifolds. We define a concept of comparison principle for elliptic PDE's on exterior domains…

math.DG2021

A Moser/Bernstein type theorem in a Lie group with a left invariant metric under a gradient decay condition

Ari Aiolfi, Leonardo Bonorino, Jaime Ripoll +2

We say that a PDE in a Riemannian manifold $M$ is geometric if,whenever $u$ is a solution of the PDE on a domain $Ω$ of $M$ , the composition $u_{ϕ} := u \circ ϕ$ is also solution on…