Scalar Curvature and Projective Embeddings, I

By Simon Donaldson. 2001

691 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f3bdaed90799d4ddae84564edf4421467bd37d71

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. G'abor Sz'ekelyhidi
2. Robert J. Berman
3. Chi Li
4. Xiuxiong Chen
5. Duong H. Phong
6. Abdellah Lahdili
7. Simon Donaldson
8. Jacob Sturm

In Geometry and Topology

1. G'abor Sz'ekelyhidi
2. Robert J. Berman
3. Chi Li
4. Xiuxiong Chen
5. Abdellah Lahdili
6. Duong H. Phong
7. Simon Donaldson
8. B. Weinkove

In Mathematical Physics

1. G'abor Sz'ekelyhidi
2. Robert J. Berman
3. Abdellah Lahdili
4. Duong H. Phong
5. Chi Li
6. Simon Donaldson
7. T. Mabuchi
8. Jacob Sturm

Citations in the corpus

• Blowing up Kähler manifolds with constant scalar curvature, II (2005, methodology): “Recent years have seen some spectacular works, inspired by the analogy with the Hitchin-Kobayashi correspondence for vector bundles, relating the existence of canonical metrics to different stability notions of manifolds [29], [8], [21], [18].”
• Complex optimal transport and the pluripotential theory of K\"ahler-Ricci solitons (2014, background): “As conjectured by Donaldson and shown in [7] the corresponding iteration Hk,m on Hk converges, in the double scaling limit where m/k → t, to the (normalized) Kähler-Ricci flow on H(−KX).”
• Space of Kähler metrics III – On the lower bound of the Calabi energy and geodesic distance (2006, background): “Donaldson[17] proved a similar lower bound in the algebraic settings.”
• Sasaki-Einstein Manifolds (2010, background): “This idea goes back to Yau [111], and has been developed by Donaldson, Tian, and others.”
• Generalized Bergman kernels on symplectic manifolds (2004, background): “[23] S. K. Donaldson, Symplectic submanifolds and almost-complex geometry, J. Diff.”
• K-stability of constant scalar curvature Kähler manifolds (2008, background): “Theorem 3.9) for a cscK polarised manifold was first proved by Donaldson [ 6 ] in the absence of continous automorphisms.”
• A generalization of the Ross--Thomas slope theory (2009, background): “We end with reviewing that for asymptotic stability of these polarized varieties, following is obtained so far by [21], [9] and [3], in comparison with Theorem 4.”