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

Showing math.DGShow all

15 papers · 1 filter

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.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…

math.DG2021

On the Size of Minimal Surfaces in $R^{4}$

Ari Aiolfi, Marc Soret, Marina Ville

The Gauss map $g$ of a surface $Σ$ in $R^{4}$ takes its values in the Grassmannian of oriented 2-planes of $R^{4}$ : $G^{+} (2, 4)$ . We give geometric criteria of stabilit…

Sequences of surfaces in 4-manifolds

Minimal tori in R4

Biharmonic Hypersurfaces in Euclidean Spaces

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

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

On the Size of Minimal Surfaces in R4

Sequences of surfaces in $4$ -manifolds

Minimal tori in $R^{4}$

On the Size of Minimal Surfaces in $R^{4}$