Integral bounds on curvature and Gromov–Hausdorff limits
By Simon Donaldson, Song Sun. 2012
50 citations recorded by the source corpus.
We develop a new approach to, and somewhat extend, results of Cheeger, Colding and Tian (Geom. Funct. Anal. 12 (2002) 873–914), which give restrictions on the singular sets that can arise as Gromov‐Hausdorff limits in the presence of integral bounds on the curvature. The foundation of this approach is provided by a rigidity result for flat singular spaces, which has independent interest.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/2dc922a0a755b72a1fe94bc9fb9b61b86b81c5a4
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In Applied Mathematics
- Tristan C. Collins
- G'abor Sz'ekelyhidi
- Chi Li
- Jian Song
- Abdellah Lahdili
- Xiaowei Wang
- Duong H. Phong
- Mattias Jonsson
In Geometry and Topology
- Tristan C. Collins
- G'abor Sz'ekelyhidi
- Chi Li
- Jian Song
- Abdellah Lahdili
- Xiaowei Wang
- Duong H. Phong
- Mattias Jonsson
Citations in the corpus
- Sasaki–Einstein metrics and K–stability (2015, background): “Following the ideas of Donaldson-Sun [40], we can then use the Hörmander technique to transplant holomorphic functions from tangent cones of GromovHausdorff limits to our non-compact cone manifold (X,ω).”