78 results found
Donaldson SK, 2018, Stability of algebraic varieties and Kahler geometry, ALGEBRAIC GEOMETRY: SALT LAKE CITY 2015, PT 1, Vol: 97, Pages: 199-221, ISSN: 2324-707X
Donaldson S, Sun S, 2017, GROMOV-HAUSDORFF LIMITS OF KAHLER MANIFOLDS AND ALGEBRAIC GEOMETRY, II, JOURNAL OF DIFFERENTIAL GEOMETRY, Vol: 107, Pages: 327-371, ISSN: 0022-040X
Donaldson S, 2016, Kahler-Einstein metrics and algebraic structures on limit spaces, Conference on Geometry and Topology, Publisher: INTERNATIONAL PRESS INC BOSTON, Pages: 85-94, ISSN: 1052-9233
Chen X, Donaldson S, Sun S, 2015, KAHLER-EINSTEIN METRICS ON FANO MANIFOLDS. I: APPROXIMATION OF METRICS WITH CONE SINGULARITIES, JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, Vol: 28, Pages: 183-197, ISSN: 0894-0347
Chen X, Donaldson S, Sun S, 2015, KAHLER-EINSTEIN METRICS ON FANO MANIFOLDS. II: LIMITS WITH CONE ANGLE LESS THAN 2 pi, JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, Vol: 28, Pages: 199-234, ISSN: 0894-0347
Chen X, Donaldson S, Sun S, 2015, KAHLER-EINSTEIN METRICS ON FANO MANIFOLDS. III: LIMITS AS CONE ANGLE APPROACHES 2 pi AND COMPLETION OF THE MAIN PROOF, JOURNAL OF THE AMERICAN MATHEMATICAL SOCIETY, Vol: 28, Pages: 235-278, ISSN: 0894-0347
Chen X, Donaldson S, Sun S, 2014, Kahler-Einstein Metrics and Stability, INTERNATIONAL MATHEMATICS RESEARCH NOTICES, Pages: 2119-2125, ISSN: 1073-7928
Chen X-X, Donaldson SK, 2014, Integral bounds on curvature and Gromov-Hausdorff limits, JOURNAL OF TOPOLOGY, Vol: 7, Pages: 543-556, ISSN: 1753-8416
Donaldson S, Sun S, 2014, Gromov-Hausdorff limits of Kahler manifolds and algebraic geometry, ACTA MATHEMATICA, Vol: 213, Pages: 63-106, ISSN: 0001-5962
Donaldson SK, 2014, b-STABILITY AND BLOW-UPS, PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, Vol: 57, Pages: 125-137, ISSN: 0013-0915
Chen X-X, Donaldson SK, 2013, VOLUME ESTIMATES FOR KAHLER-EINSTEIN METRICS: THE THREE-DIMENSIONAL CASE, JOURNAL OF DIFFERENTIAL GEOMETRY, Vol: 93, Pages: 175-189, ISSN: 0022-040X
Chen X-X, Donaldson SK, 2013, VOLUME ESTIMATES FOR KAHLER-EINSTEIN METRICS AND RIGIDITY OF COMPLEX STRUCTURES, JOURNAL OF DIFFERENTIAL GEOMETRY, Vol: 93, Pages: 191-201, ISSN: 0022-040X
Donaldson S, 2012, Kahler metrics with cone singularities along a divisor
We develop some foundations for the study of Kahler-Einstein metrics withcone singularities transverse to a divisor. The main goal is a treatment of thedeformation of the cone angle.
Donaldson S, 2010, Calabi-Yau metrics on Kummer surfaces as a model glueing problem
This is an expository paper which aims to give a simple proof of theexistence of Ricci-flat metrics on certain K3 surfaces, as an illustration ofgeneral "glueing" techniques.
Donaldson S, 2010, Stability, birational transformations and the Kahler-Einstein problem
We define a new notion of "b-stability" for a polarised algebraic variety,adapted to the existence problem for Kahler-Einstein metrics on Fano manifolds.
Donaldson SK, 2009, Constant Scalar Curvature Metrics on Toric Surfaces, GEOMETRIC AND FUNCTIONAL ANALYSIS, Vol: 19, Pages: 83-136, ISSN: 1016-443X
Donaldson SK, 2009, Some Numerical Results in Complex Differential Geometry, PURE AND APPLIED MATHEMATICS QUARTERLY, Vol: 5, Pages: 571-618, ISSN: 1558-8599
Bunch RS, Donaldson SK, 2008, Numerical approximations to extremal metrics on toric surfaces
We give some detailed numerical information about extremal metrics on fourdifferent toric surfaces. These are sample of many other cases which can betreated using a computer programme outlined in the paper.
Donaldson SK, 2008, Some problems in differential geometry and topology, NONLINEARITY, Vol: 21, Pages: T157-T164, ISSN: 0951-7715
Donaldson SK, 2008, Extremal metrics on toric surfaces: A continuity method, JOURNAL OF DIFFERENTIAL GEOMETRY, Vol: 79, Pages: 389-432, ISSN: 0022-040X
Donaldson SK, 2008, Kahler geometry on toric manifolds, and some other manifolds with large symmetry
This is an expository article. Among other topics, we discuss the existenceof Kahler-Ricci soliton metrics on toric Fano manifolds, and Kahler-Einsteinmetrics on deformations of the Mukai-Umemura 3-fold
Donaldson SK, 2008, A generalised Joyce construction for a family of nonlinear partial differential equations
We explain a simple construction of solutions to a family of PDE's in twodimensions which includes that defining zero scalar curvature Kahler metrics,with two Killing fields, and the affine maximal equation.
Donaldson SK, 2007, Nahm's equations and free-boundary problems
This paper is a discussion of relations between some free-boundary problemsand infinite dimensional Lie groups; particularly a version of Nahm's equationsfor the group of Hamiltonian diffeomorphisms in two dimensions.
Donaldson SK, 2007, A note on the α-invariant of the Mukai-Umemura 3-fold
We give an elementary argument to compute the $\alpha$-invariant of this Fano3-fold, which implies the existence of a Kahler-Einstein metric.
Donaldson SK, 2007, Lie algebra theory without algebra
This is an expository paper in which we explain how basic, standard, resultsabout simple Lie algebras can be obtained by geometric arguments, followingideas of Cartan, Richardson and others.
Donaldson S, Fine J, 2006, Tonic anti-self-dual 4-manifolds via complex geometry, MATHEMATISCHE ANNALEN, Vol: 336, Pages: 281-309, ISSN: 0025-5831
Donaldson SK, 2006, Two-forms on four-manifolds and elliptic equations
We define a general class of elliptic equations for 2-forms on 4-manifolds,of which the complex Monge-Ampere equation is a prototype. We obtain someregularity results and discuss various connections (some speculative) withmodern symplectic 4-manifold theory.
Donaldson SK, 2006, Extremal metrics on toric surfaces, I
The paper develops a continiuty method for solutions of the Abreu equation,which include extremal metrics on toric surfaces. Results are obtained,assuming a hypothesis (the "M-condition") on the solutions.
Auroux D, Donaldson SK, Katzarkov L, 2005, Singular Lefschetz pencils, GEOMETRY & TOPOLOGY, Vol: 9, Pages: 1043-1114, ISSN: 1364-0380
Donaldson SK, 2005, Interior estimates for solutions of Abreu's equation, COLLECTANEA MATHEMATICA, Vol: 56, Pages: 103-142, ISSN: 0010-0757
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