Marco A. M. Guaraco

activity

20152026

most citedMultiplicity one and strictly stable Allen-Cahn minimal hypersurfaces

7 citations · 11 across the 9 of their papers we have counts for

collaborators

10 papers

math.DG2026

White's cone over the Möbius band is area-minimising

Marco A. M. Guaraco, Davide Parise

We prove that the cone $C (Σ)$ in $R^{4}$ over a suitable minimal Möbius band $Σ \subset S^{3}$ is locally mass-minimising with coefficients in $Z_{2}$ . This proves…

math.DG2026

Integral curvature estimates and geodesic limits for stable abelian Higgs fields

Marco Badran, Marco A. M. Guaraco, Aria Halavati

We prove that, on closed three-manifolds, the limit interface of a sequence of stable abelian Higgs critical points with uniformly bounded energy is a finite union of smooth closed…

math.AP2026

A two-dimensional Allen-Cahn theory for interfaces with boundary

Marco Badran, Manuel del Pino, Marco A. M. Guaraco

We develop a two-dimensional Allen-Cahn theory for interfaces with boundary in the line-bundle framework introduced by Fröhlich and Struwe. The central new object is a model soluti…

math.DG2023

Plateau's problem via the Allen--Cahn functional

Marco A. M. Guaraco, Stephen Lynch

Let $Γ$ be a compact codimension-two submanifold of $R^{n}$ , and let $L$ be a nontrivial real line bundle over $X = R^{n} ∖ Γ$ . We study the Allen--Cahn funct…

math.DG2021

Mean curvature flow in homology and foliations of hyperbolic $3$ -manifolds

Marco A. M. Guaraco, Vanderson Lima, Franco Vargas Pallete

We study global aspects of the mean curvature flow of non-separating hypersurfaces $S$ in closed manifolds. For instance, if $S$ has non-vanishing mean curvature, we show its level…

math.AP2020★ 3 cited

Ground states of semilinear elliptic equations

Rayssa Caju, Pedro Gaspar, Marco A. M. Guaraco +1

We study solutions of $Δ u - F^{'} (u) = 0$ , where the potential $F$ can have an arbitrary number of wells at arbitrary heights, including bottomless wells with subcritical decay. In our…

math.DG2019★ 7 cited

Multiplicity one and strictly stable Allen-Cahn minimal hypersurfaces

Marco A. M. Guaraco, Fernando C. Marques, Andre Néves

We show that strictly stable components of Allen-Cahn minimal hypersurfaces always occur with multiplicity one. We also establish the uniqueness of solutions converging to nondegen…

math.DG2018★ 1 cited

The Weyl Law for the phase transition spectrum and density of limit interfaces

Pedro Gaspar, Marco A. M. Guaraco

We prove a Weyl Law for the phase transition spectrum based on the techniques of Liokumovich-Marques-Neves. As an application we give phase transition adaptations of the proofs of…

math.DG2016

The Allen-Cahn equation on closed manifolds