Spiro Karigiannis

activity

20032026

most citedFlows of G_2 Structures, I

91 citations · 424 across the 32 of their papers we have counts for

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32 papers · 1 filter

math.DG2026

Montel's theorem and tautness in calibrated geometry

Anton Iliashenko, Spiro Karigiannis, Jesse Madnick

We relate the hyperbolicity of a calibrated manifold $(X, ϕ)$ to the analytic properties of the space of Smith immersions $SmIm (B^{k}, X)$ from the Poincare $k$ -ball into $X…

math.DG2025

Flows of conformally coclosed $G_{2}$ -structures with dilaton

Spiro Karigiannis, Sébastien Picard, Caleb Suan

We study flows of $G_{2}$ -structures guided by the principle of dimensional reduction: natural geometric flows in $G_{2}$ -geometry reduce to natural flows in complex geometry. Our main…

math.DG2025

Non-squeezing and capacities for some calibrated geometries

Kain Dineen, Spiro Karigiannis

It was shown by Barron--Shafiee that an analogue of Gromov's non-squeezing theorem holds for affine maps which preserve a power $ω^{k}$ of the symplectic form $ω$ on $\mathbb{R}^{2n}…

math.DG2025

Holomorphicity of parabolic stable minimal surfaces of high codimension

Da Rong Cheng, Spiro Karigiannis, Jesse Madnick

A classical theorem of Micallef says that if $F : (Σ, g) \to R^{4}$ is a stable minimal immersion of an oriented $2$ -dimensional complete Riemannian manifold (that is p…

math.DG2025

Hodge theoretic results for nearly Kähler manifolds in all dimensions

Michael Albanese, Spiro Karigiannis, Lucía Martín-Merchán +1

We generalize to nearly Kähler manifolds of arbitrary dimensions most of the Hodge-theoretic results for nearly Kähler $6$ -manifolds that were established by Verbitsky. In particul…

math.DG2025

BRIDGES Lectures: Flows of geometric structures, especially $G_{2}$ -structures

Spiro Karigiannis

The BRIDGES meeting in gauge theory, extremal structures, and stability was held June 2024 at l'Institut d'Études Scientifiques de Cargèse in Corsica, organized by Daniele Faenzi,…

math.DG2024

Cohomogeneity one solitons for the isometric flow of $G_{2}$ -structures

Thomas A. Ivey, Spiro Karigiannis

We consider the existence of cohomogeneity one solitons for the isometric flow of $G_{2}$ -structures on the following classes of torsion-free $G_{2}$ -manifolds: the Euclidean $R^{7}$ wit…

math.DG2023★ 1 cited

A special class of $k$ -harmonic maps inducing calibrated fibrations

Anton Iliashenko, Spiro Karigiannis

We consider two special classes of $k$ -harmonic maps between Riemannian manifolds which are related to calibrated geometry, satisfying a first order fully nonlinear PDE. The first…

math.DG2023★ 4 cited

Flows of $G_{2}$ -structures, II: Curvature, torsion, symbols, and functionals

Shubham Dwivedi, Panagiotis Gianniotis, Spiro Karigiannis

We continue the investigation of general geometric flows of $G_{2}$ -structures initiated by the third author in "Flows of $G_{2}$ -structures, I." Specifically, we determine the possibl…

math.DG2023

Extrinsic geometry of calibrated submanifolds

Spiro Karigiannis, Lucía Martín-Merchán

Given a calibration $α$ whose stabilizer acts transitively on the Grassmanian of calibrated planes, we introduce a nontrivial Lie-theoretic condition on $α$ , which we call complian…

math.DG2023★ 1 cited

Calibrated Geometry in Hyperkahler Cones, 3-Sasakian Manifolds, and Twistor Spaces

Benjamin Aslan, Spiro Karigiannis, Jesse Madnick

We systematically study calibrated geometry in hyperkähler cones $C^{4 n + 4}$ , their 3-Sasakian links $M^{4 n + 3}$ , and the corresponding twistor spaces $Z^{4 n + 2}$ , emphasizing the rel…

math.DG2022★ 1 cited

Observations about the Lie algebra $g_{2} \subset so (7)$ , associative $3$ -planes, and $so (4)$ subalgebras

Max Chemtov, Spiro Karigiannis

We make several observations relating the Lie algebra $g_{2} \subset so (7)$ , associative $3$ -planes, and $so (4)$ subalgebras. Some are likely well-kn…

math.DG2022★ 2 cited

A variational characterization of calibrated submanifolds

Da Rong Cheng, Spiro Karigiannis, Jesse Madnick

Let $M$ be a fixed compact oriented embedded submanifold of a manifold $M$ . Consider the volume $V (g) = \int_{M} vol_{(M, g)}$ as a function…

math.DG2020

Twisted-Austere Submanifolds in Euclidean Space

Thomas A. Ivey, Spiro Karigiannis

A twisted-austere $k$ -fold $(M, μ)$ in $R^{n}$ consists of a $k$ -dimensional submanifold $M$ of $R^{n}$ together with a closed $1$ -form $μ$ on $M$ such that the `twiste…

math.DG2020★ 9 cited

Bryant-Salamon $G_{2}$ manifolds and coassociative fibrations

Spiro Karigiannis, Jason D. Lotay

Bryant-Salamon constructed three 1-parameter families of complete manifolds with holonomy $G_{2}$ which are asymptotically conical to a holonomy $G_{2}$ cone. For eac…

math.DG2019★ 9 cited

Introduction to $G_{2}$ geometry

Spiro Karigiannis

These notes give an informal and leisurely introduction to $G_{2}$ geometry for beginners. A special emphasis is placed on understanding the special linear algebraic structu…

math.DG2019★ 8 cited

Bubble Tree Convergence of Conformally Cross Product Preserving Maps

Da Rong Cheng, Spiro Karigiannis, Jesse Madnick

We study a class of weakly conformal $3$ -harmonic maps, called associative Smith maps, from $3$ -manifolds into $7$ -manifolds that parametrize associative $3$ -folds in Riemannian $7…

math.DG2019★ 17 cited

A gradient flow of isometric $G_{2}$ structures

Shubham Dwivedi, Panagiotis Gianniotis, Spiro Karigiannis

We study a flow of $G_{2}$ structures which induce the same Riemannian metric which is the negative gradient flow of an energy functional. We prove Shi-type estimates for the torsion…

math.DG2018★ 2 cited

The $L_{B}$ -cohomology on compact torsion-free $G_{2}$ manifolds and an application to 'almost' formality

Ki Fung Chan, Spiro Karigiannis, Chi Cheuk Tsang

We study a cohomology theory $H_{φ}^{∙}$ , called the $L_{B}$ -cohomology, on compact torsion-free $G_{2}$ -manifolds. We show that $H_{φ}^{k} ≅ H_{dR}^{k}$ f…

math.DG2017★ 1 cited

Cohomologies on almost complex manifolds and the $\partial \partial ˉ$ -lemma

Ki Fung Chan, Spiro Karigiannis, Chi Cheuk Tsang

We study cohomologies on an almost complex manifold $(M, J)$ , defined using the Nijenhuis-Lie derivations $L_{J}$ and $L_{N}$ induced from the almost complex struct…

math.DG2017★ 34 cited

A new construction of compact torsion-free $G_{2}$ -manifolds by gluing families of Eguchi-Hanson spaces

Dominic Joyce, Spiro Karigiannis

We give a new construction of compact Riemannian 7-manifolds with holonomy $G_{2}$ . Let $M$ be a torsion-free $G_{2}$ -manifold (which can have holonomy a proper subgroup of $G_{2}$ ) such…

math.DG2012★ 21 cited

Deformation theory of G_2 conifolds

Spiro Karigiannis, Jason Lotay

We consider the deformation theory of asymptotically conical (AC) and of conically singular (CS) $G_{2}$ -manifolds. In the AC case, we show that if the rate of convergence $ν$ to the…

math.DG2011★ 9 cited

Deformations of calibrated subbundles of Euclidean spaces via twisting by special sections

Spiro Karigiannis, Nat Chun-Ho Leung

We extend the "bundle constructions" of calibrated submanifolds, due to Harvey--Lawson in the special Lagrangian case, and to Ionel--Karigiannis--Min-Oo in the cases of exceptional…

math.DG2011★ 47 cited

Soliton solutions for the Laplacian coflow of some $G_{2}$ -structures with symmetry

Spiro Karigiannis, Benjamin McKay, Mao-Pei Tsui

We consider the Laplacian "co-flow" of $G_{2}$ -structures: $\frac{d}{d t} ψ = - Δ_{d} ψ$ where $ψ$ is the dual 4-form of a $G_{2}$ -structure $ϕ$ and $Δ_{d}$ is the Hodge Laplacian on forms.…

Montel's theorem and tautness in calibrated geometry

Flows of conformally coclosed G2​-structures with dilaton

Non-squeezing and capacities for some calibrated geometries

Holomorphicity of parabolic stable minimal surfaces of high codimension

Hodge theoretic results for nearly Kähler manifolds in all dimensions

BRIDGES Lectures: Flows of geometric structures, especially G2​-structures

Cohomogeneity one solitons for the isometric flow of G2​-structures

A special class of k-harmonic maps inducing calibrated fibrations

Flows of G2​-structures, II: Curvature, torsion, symbols, and functionals

Extrinsic geometry of calibrated submanifolds

Calibrated Geometry in Hyperkahler Cones, 3-Sasakian Manifolds, and Twistor Spaces

Observations about the Lie algebra g2​⊂so(7), associative 3-planes, and so(4) subalgebras

A variational characterization of calibrated submanifolds

Twisted-Austere Submanifolds in Euclidean Space

Bryant-Salamon G2​ manifolds and coassociative fibrations

Introduction to G2​ geometry

Bubble Tree Convergence of Conformally Cross Product Preserving Maps

A gradient flow of isometric G2​ structures

The LB​-cohomology on compact torsion-free G2​ manifolds and an application to 'almost' formality

Cohomologies on almost complex manifolds and the ∂∂ˉ-lemma

A new construction of compact torsion-free G2​-manifolds by gluing families of Eguchi-Hanson spaces

Deformation theory of G_2 conifolds

Deformations of calibrated subbundles of Euclidean spaces via twisting by special sections

Soliton solutions for the Laplacian coflow of some G2​-structures with symmetry

Flows of conformally coclosed $G_{2}$ -structures with dilaton

BRIDGES Lectures: Flows of geometric structures, especially $G_{2}$ -structures

Cohomogeneity one solitons for the isometric flow of $G_{2}$ -structures

A special class of $k$ -harmonic maps inducing calibrated fibrations

Flows of $G_{2}$ -structures, II: Curvature, torsion, symbols, and functionals

Observations about the Lie algebra $g_{2} \subset so (7)$ , associative $3$ -planes, and $so (4)$ subalgebras

Bryant-Salamon $G_{2}$ manifolds and coassociative fibrations

Introduction to $G_{2}$ geometry

A gradient flow of isometric $G_{2}$ structures

The $L_{B}$ -cohomology on compact torsion-free $G_{2}$ manifolds and an application to 'almost' formality

Cohomologies on almost complex manifolds and the $\partial \partial ˉ$ -lemma

A new construction of compact torsion-free $G_{2}$ -manifolds by gluing families of Eguchi-Hanson spaces

Soliton solutions for the Laplacian coflow of some $G_{2}$ -structures with symmetry