Zobrazeno 1 - 10
of 135
pro vyhledávání: '"Donaldson, Simon"'
Autor:
Donaldson, Simon, Lehmann, Fabian
We develop the deformation theory of Calabi-Yau threefolds, by which we mean 3-dimensional complex manifolds with a nowhere-vanishing holomorphic 3-form, on manifolds with boundary. The boundary data is a closed, real 3-form on the 5-dimensional boun
Externí odkaz:
http://arxiv.org/abs/2403.15184
Autor:
Donaldson, Simon, Lehmann, Fabian
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 analogues of the affine isoperimetric inequality. In the last section of th
Externí odkaz:
http://arxiv.org/abs/2305.09932
Autor:
Donaldson, Simon, Lehmann, Fabian
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 induces a given closed 3-form on the 5-manifold. We define an open se
Externí odkaz:
http://arxiv.org/abs/2210.16208
Autor:
Donaldson, Simon
This is an expository article discussing some of the work of Uhlenbeck, focusing mainly on work concerning harmonic maps and Yang-Mills fields.
Comment: To appear in H. Holden and R. Piene (eds.): "The Abel Prize 2018-2022" Spinger 2023
Comment: To appear in H. Holden and R. Piene (eds.): "The Abel Prize 2018-2022" Spinger 2023
Externí odkaz:
http://arxiv.org/abs/2205.08970
Autor:
Donaldson, Simon
This is an expository article on the 1978 Atiyah-Drinfeld-Hitchin-Manin construction of Yang-Mills instanton connections over the 4-sphere.
Comment: Based on an online talk, CMSA, Harvard May 2020. To appear in series "Literature and History of
Comment: Based on an online talk, CMSA, Harvard May 2020. To appear in series "Literature and History of
Externí odkaz:
http://arxiv.org/abs/2205.08639
Autor:
Donaldson, Simon
This article is a review of parts of Atiyah's work, mainly from the periods 1952-1958 and 1976-1990.
Comment: This was one of three articles on Atiyah's work which appeared in the Bull. Amer. Math. Soc Vol. 58, 2021
Comment: This was one of three articles on Atiyah's work which appeared in the Bull. Amer. Math. Soc Vol. 58, 2021
Externí odkaz:
http://arxiv.org/abs/2205.08631
Autor:
Donaldson, Simon
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 elliptic partial differential equations. In the second part we discuss
Externí odkaz:
http://arxiv.org/abs/2205.08624
Autor:
Donaldson, Simon, Scaduto, Christopher
We discuss a model for associative submanifolds in $G_{2}$-manifolds with K3 fibrations, in the adiabatic limit. The model involves graphs in a 3-manifold whose edges are locally gradient flow lines. We show that this model produces analogues of know
Externí odkaz:
http://arxiv.org/abs/2004.07314
Autor:
Donaldson, Simon
We consider harmonic sections of a bundle over the complement of a codimension 2 submanifold in a Riemannian manifold, which can be thought of as multivalued harmonic functions. We prove a result to the effect that these are stable under small deform
Externí odkaz:
http://arxiv.org/abs/1912.08274