Gonçalo Oliveira

activity

20132026

most citedMonopoles on the Bryant-Salamon

G_{2}

Manifolds

25 citations · 79 across the 23 of their papers we have counts for

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20 papers · 1 filter

math.DG2026

The mean curvature blows up at nondegenerate neck pinch singularities of Lagrangian mean curvature flow

Jason D. Lotay, Goncalo Oliveira

We prove that at any nondegenerate neck pinch singularity of Lagrangian mean curvature flow of surfaces the mean curvature becomes unbounded, with control on the blow-up rate.

math.DG2026

Large mass limits of $G_{2}$ and Calabi--Yau monopoles: calibrated concentration, Higgs zeros, and abelianization

Daniel Fadel, Goncalo Oliveira

We study large mass monopoles with structure group $SU (2)$ or $SO (3)$ on asymptotically conical $G_{2}$ -manifolds and Calabi--Yau $3$ -folds, with fixed asy…

math.DG2023

Neck pinch singularities and Joyce conjectures in Lagrangian mean curvature flow with circle symmetry

Jason D. Lotay, Goncalo Oliveira

In this article we consider the Lagrangian mean curvature flow of compact, circle-invariant, almost calibrated Lagrangian surfaces in hyperkähler 4-manifolds with circle symmetry.…

math.DG2023

Electrostatics and geodesics on $K 3$ surfaces

Goncalo Oliveira

Motivated by some conjectures originating in the Physics literature, we use Foscolo's construction of Ricci-flat Kahler metrics on K3 surfaces to locate, with high precision, sever…

math.DG2020★ 1 cited

The asymptotic geometry of $G_{2}$ -monopoles

Daniel Fadel, Ákos Nagy, Gonçalo Oliveira

This article investigates the asymptotics of $G_{2}$ -monopoles. First, we prove that when the underlying $G_{2}$ -manifold is nonparabolic (i.e. admits a positive Green's func…

math.DG2020★ 1 cited

Examples of deformed G_2-instantons/Donaldson-Thomas connections

Jason D. Lotay, Goncalo Oliveira

In this note, we provide the first non-trivial examples of deformed G_2-instantons, originally called deformed Donaldson-Thomas connections. As a consequence, we see how deformed G…

math.DG2020

The DT-instanton equation on almost Hermitian 6-manifolds

Gavin Ball, Goncalo Oliveira

This article investigates a set of partial differential equations, the DT-instanton equations, whose solutions can be regarded as a generalization of the notion of Hermitian-Yang-M…

math.DG2020

Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz

Jason D. Lotay, Goncalo Oliveira

The Gibbons-Hawking ansatz provides a large family of circle-invariant hyperkaehler 4-manifolds, and thus Calabi-Yau 2-folds. In this setting, we prove versions of the Thomas conje…

math.DG2019★ 1 cited

The Kapustin--Witten equations on ALE and ALF gravitational instantons

Ákos Nagy, Gonçalo Oliveira

We study solutions to the Kapustin--Witten equations on ALE and ALF gravitational instantons. On any such space and for any compact structure group, we prove asymptotic estimates f…

math.DG2019

The Haydys monopole equation

Ákos Nagy, Gonçalo Oliveira

We study complexified Bogomolny monopoles using the complex linear extension of the Hodge star operator; these monopoles can be interpreted as solutions to the Bogomolny equation w…

math.DG2018★ 2 cited

$G_{2}$ -instantons on noncompact $G_{2}$ -manifolds: results and open problems

Jason Lotay, Goncalo Oliveira

We survey the known existence and non-existence results for $G_{2}$ -instantons on non-compact cohomogeneity-1 $G_{2}$ -manifolds and their consequences, including an explicit example of…

math.DG2018

Yang-Mills flow on special-holonomy manifolds

Goncalo Oliveira, Alex Waldron

This paper develops Yang-Mills flow on Riemannian manifolds with special holonomy. By analogy with the second-named author's thesis, we find that a supremum bound on a certain curv…

math.DG2018★ 4 cited

The limit of large mass monopoles

Daniel Fadel, Goncalo Oliveira

In this paper, we consider finite energy $SU (2)$ monopoles on an asymptotically conical, oriented Riemannian $3$ -manifold with one end. The connected components of the mod…

math.DG2017

From vortices to instantons on the Euclidean Schwarzschild manifold

Ákos Nagy, Gonçalo Oliveira

The first irreducible solution of the $SU (2)$ self-duality equations on the Euclidean Schwarzschild (ES) manifold was found by Charap and Duff in 1977, only 2 years later…

math.DG2016★ 10 cited

Gauge theory on Aloff-Wallach spaces

Gavin Ball, Goncalo Oliveira

For gauge groups $U (1)$ and $S O (3)$ we classify invariant $G_{2}$ -instantons for homogeneous coclosed $G_{2}$ -structures on Aloff-Wallach spaces $X_{k, l}$ . As a consequence, we give ex…

math.DG2016★ 2 cited

$G_{2}$ -monopoles with singularities (examples)

Goncalo Oliveira

$G_{2}$ -monopoles are solutions to gauge theoretical equations on $G_{2}$ -manifolds. If the $G_{2}$ -manifolds under consideration are compact, then any irreducible $G_{2}$ -monopole must ha…

math.DG2016★ 1 cited

Gerbes on $G_{2}$ Manifolds

Goncalo Oliveira

On a projective complex manifold, the Abelian group of Divisors maps surjectively onto that of holomorphic line bundles (the Picard group). On a $G_{2}$ -manifold we use coassociative…

math.DG2014★ 12 cited

Monopoles on 3 dimensional AC manifolds

Goncalo Oliveira

We construct monopoles in any asymptotically conical (AC) $3$ -manifold $X$ with $b^{2} (X) = 0$ . For sufficiently large mass, our construction covers an open set in the moduli space of…

math.DG2014★ 10 cited

Calabi-Yau Monopoles for the Stenzel Metric

Goncalo Oliveira

We construct the first nontrivial examples of Calabi-Yau monopoles. Our main interest on these, comes from Donaldson and Segal's suggestion \cite{Donaldson2009} that it may be poss…

math.DG2013★ 25 cited

Monopoles on the Bryant-Salamon $G_{2}$ Manifolds

Goncalo Oliveira

$G_{2}$ -Monopoles are solutions to gauge theoretical equations on noncompact $7$ -manifolds of $G_{2}$ holonomy. We shall study this equation on the $3$ Bryant-Salamon manifolds. We con…

The mean curvature blows up at nondegenerate neck pinch singularities of Lagrangian mean curvature flow

Large mass limits of G2​ and Calabi--Yau monopoles: calibrated concentration, Higgs zeros, and abelianization

Neck pinch singularities and Joyce conjectures in Lagrangian mean curvature flow with circle symmetry

Electrostatics and geodesics on K3 surfaces

The asymptotic geometry of G2​-monopoles

Examples of deformed G_2-instantons/Donaldson-Thomas connections

The DT-instanton equation on almost Hermitian 6-manifolds

Special Lagrangians, Lagrangian mean curvature flow and the Gibbons-Hawking ansatz

The Kapustin--Witten equations on ALE and ALF gravitational instantons

The Haydys monopole equation

G2​-instantons on noncompact G2​-manifolds: results and open problems

Yang-Mills flow on special-holonomy manifolds

The limit of large mass monopoles

From vortices to instantons on the Euclidean Schwarzschild manifold

Gauge theory on Aloff-Wallach spaces

G2​-monopoles with singularities (examples)

Gerbes on G2​ Manifolds

Monopoles on 3 dimensional AC manifolds

Calabi-Yau Monopoles for the Stenzel Metric

Monopoles on the Bryant-Salamon G2​ Manifolds

Large mass limits of $G_{2}$ and Calabi--Yau monopoles: calibrated concentration, Higgs zeros, and abelianization

Electrostatics and geodesics on $K 3$ surfaces

The asymptotic geometry of $G_{2}$ -monopoles

$G_{2}$ -instantons on noncompact $G_{2}$ -manifolds: results and open problems

$G_{2}$ -monopoles with singularities (examples)

Gerbes on $G_{2}$ Manifolds

Monopoles on the Bryant-Salamon $G_{2}$ Manifolds