131 citations · 736 across the 37 of their papers we have counts for
41 papers · 1 filter
Volume functionals on pseudoconvex hypersurfaces
Simon Donaldson, Fabian Lehmann
We study an intrinsic volume form defined on a pseudoconvex hypersurface in a complex Calabi-Yau manifold. We compute first and second variation formulae and discuss possible analo…
Closed 3-forms in five dimensions and embedding problems
Simon Donaldson, Fabian Lehmann
We consider the question if a five dimensional manifold can be embedded into a Calabi-Yau manifold of complex dimension three such that the real part of the holomorphic volume form…
A journey through the mathematical world of Karen Uhlenbeck
Simon Donaldson
This is an expository article discussing some of the work of Uhlenbeck, focusing mainly on work concerning harmonic maps and Yang-Mills fields.
The ADHM construction of Yang-Mills instantons
Simon Donaldson
This is an expository article on the 1978 Atiyah-Drinfeld-Hitchin-Manin construction of Yang-Mills instanton connections over the 4-sphere.
Fredholm topology and enumerative geometry: reflections on some words of Michael Atiyah
Simon Donaldson
The first part of this article is a short and selective survey of developments in differential and algebraic geometry from the 1980's involving enumerative questions and nonlinear…
Associative submanifolds and gradient cycles
Simon Donaldson, Christopher Scaduto
We discuss a model for associative submanifolds in -manifolds with K3 fibrations, in the adiabatic limit. The model involves graphs in a 3-manifold whose edges are locally g…