25 citations · 44 across the 14 of their papers we have counts for
17 papers
Nef Hattori classes and products of projective lines
Daniel Álvarez, Andrew Clarke, Eduardo González
Let \(X\) be a smooth connected complex projective variety with an effective algebraic \(\mathbb C^{\times}\)-action, a nonempty finite fixed locus whose weights are \(\pm1\). We s…
Geodesics With Unbounded Speed on Fluctuating Surfaces
Andrew Clarke
We construct time-periodic fluctuating surfaces in such that the corresponding nonautonomous geodesic flow has orbits along which the energy, and thus t…
G-instantons on -step nilpotent Lie groups
Andrew Clarke, Viviana del Barco, Andrés J. Moreno
We study the G-instanton condition for a family of metric connections arisen from the characteristic connection, on -dimensional -step nilpotent Lie groups with left-inva…
Semi-stability and local wall-crossing for hermitian Yang-Mills connections
Andrew Clarke, Carl Tipler
We consider a sufficiently smooth semi-stable holomorphic vector bundle over a compact Kähler manifold. Assuming the automorphism group of its graded object to be abelian, we provi…
Blowing-up Hermitian Yang--Mills connections
Andrew Clarke, Carl Tipler
We investigate hermitian Yang--Mills connections for pullback vector bundles on blow-ups of Kähler manifolds along submanifolds. Under some mild asumptions on the graded object of…
Topological Shadowing Methods in Arnold Diffusion: Weak Torsion and Multiple Time Scales
Andrew Clarke, Jacques Fejoz, Marcel Guardia
Consider a symplectic map which possesses a normally hyperbolic invariant manifold of any even dimension with transverse homoclinic channels. We develop a topological shadowing arg…
-Dual solutions and infinitesimal moduli of the -Strominger system
Andrew Clarke, Mario Garcia-Fernandez, Carl Tipler
We consider -structures with torsion coupled with -instantons, on a compact -dimensional manifold. The coupling is via an equation for -forms which appears in super…
Equivariant stable sheaves and toric GIT
Andrew Clarke, Carl Tipler
For (X,L) a polarized toric variety and G a torus of automorphisms of (X,L), denote by Y the GIT quotient X/G. We define a family of fully faithful functors from the category of to…
Generic Properties of Geodesic Flows on Analytic Hypersurfaces of Euclidean Space
Andrew Clarke
Consider the geodesic flow on a real-analytic closed hypersurface of , equipped with the standard Euclidean metric. The flow is entirely determined by the manifol…
Arnold Diffusion in Multi-Dimensional Convex Billiards
Andrew Clarke, Dmitry Turaev
Consider billiard dynamics in a strictly convex domain, and consider a trajectory that begins with the velocity vector making a small positive angle with the boundary. Lazutkin pro…
-Instantons from evolution equations
Andrew Clarke, Gonçalo Oliveira
In this paper we study -instantons on asymptotically conical -orbifolds (and manifolds) obtained by filling in certain squashed -Sasakian -manif…
Moduli of structures and the Strominger system in dimension 7
Andrew Clarke, Mario Garcia-Fernandez, Carl Tipler
We consider structures with torsion coupled with -instantons, on a compact -dimensional manifold. The coupling is via an equation for -forms which appears in super…
Instantons on the exceptional holonomy manifolds of Bryant and Salamon
Andrew Clarke
We give a construction of and instantons on exceptional holonomy manifolds constructed by Bryant and Salamon, by using an ansatz of spherical symmetry coming from t…
Lower bounds on the modified K-energy and complex deformations
Andrew Clarke, Carl Tipler
Let (X,L) be a polarized Kähler manifold that admits an extremal Kähler metric in c1(L). We show that on a nearby polarized deformation that preserves the symmetry induced by the e…
Holonomy Groups in Riemannian Geometry
Andrew Clarke, Bianca Santoro
Lecture notes for the minicourse "Holonomy Groups in Riemannian geometry", a part of the XVII Brazilian School of Geometry, to be held at UFAM (Amazonas, Brazil), in July of 2012.
Minimal Surfaces in G2 Manifolds
Andrew Clarke
We consider immersions of a Riemann surface into a manifold with -holonomy and give criteria for them to be conformal and harmonic, in terms of an associated Gauss map.
The Perron Method and the Non-Linear Plateau Problem
Andrew Clarke, Graham Smith
We describe a novel technique for solving the Plateau problem for constant curvature hypersurfaces based on recent work of Harvey and Lawson. This is illustrated by an existence th…