Journal Article10.1007/S00220-016-2661-4
Mass in Kähler Geometry
Hans-Joachim Hein,Claude LeBrun +1 more
37
TL;DR: In this paper, a simple, explicit formula for the mass of any asymptotically locally Euclidean (ALE) Kahler manifold, assuming only the sort of weak fall-off conditions required for the Mass to actually be well-defined, is presented.
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Abstract: We prove a simple, explicit formula for the mass of any asymptotically locally Euclidean (ALE) Kahler manifold, assuming only the sort of weak fall-off conditions required for the mass to actually be well-defined. For ALE scalar-flat Kahler manifolds, the mass turns out to be a topological invariant, depending only on the underlying smooth manifold, the first Chern class of the complex structure, and the Kahler class of the metric. When the metric is actually AE (asymptotically Euclidean), our formula not only implies a positive mass theorem for Kahler metrics, but also yields a Penrose-type inequality for the mass.
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Citations
Classification of asymptotically conical Calabi-Yau manifolds
Ronan Conlon,Hans-Joachim Hein +1 more
- 03 Jan 2022
TL;DR: In this article , a complete classification of all smooth complete Calabi-Yau manifolds asymptotic to some given Calabi Yau cone at a polynomial rate at infinity is given.
Existence and compactness theory for ale scalar-flat kähler surfaces
Jiyuan Han,Jeff A. Viaclovsky +1 more
TL;DR: In this paper, it was shown that a noncollapsed sequence of asymptotically locally Euclidean (ALE) scalar-flat Kahler metrics on a minimal Kahler surface whose Kahler classes stay in a compact subset of the interior of the cone must have a convergent subsequence.
•Posted Content
On the classification of ALE K\"ahler manifolds
TL;DR: The underlying complex structure of an ALE K\"ahler manifold is exhibited as a resolution of a deformation of an isolated quotient singularity as discussed by the authors, and there exist only finitely many diffeomorphism types of minimal ALE K''ahler surfaces with a given group at infinity.
Gromov-Hausdorff limits and Holomorphic isometries
Claudio Arezzo,Chao-Jun Li,Andrea Loi +2 more
- 28 Jun 2023
TL;DR: In this paper , pointed Gromov-Hausdorff convergence of sequences of K\"ahler submanifolds of a fixed K''ahler ambient space is studied.
References
•Book
Principles of Algebraic Geometry
Phillip Griffiths,Joe Harris +1 more
- 01 Jan 1978
TL;DR: In this paper, a comprehensive, self-contained treatment of complex manifold theory is presented, focusing on results applicable to projective varieties, and including discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex.
9.1K
•Book
Compact Complex Surfaces
Wolf Barth
- 01 Jan 1984
TL;DR: In this article, the authors describe the topology and algebraic properties of complex surfaces, including the following properties: 1. The Projective Plane, 2. The Jacobian Fibration, 3. Hodge Theory on Surfaces, 4. Inequahties for Hodge Numbers, 5. Holomorphic Vector Bundles, Serre Duality and Riemann-Roch Theorem.
3K
A new proof of the positive energy theorem
TL;DR: In this article, a new proof of the positive energy theorem of classical general relativity was given and it was shown that there are no asymptotically Euclidean gravitational instantons.
The Yamabe problem
TL;DR: The present book is not really intended as an updated exposition or extension of the theory in those volumes, but brings in developments of the Theory as necessary and as inspired by a number of applications that are discussed throughout the book.
•Book
Compact Manifolds with Special Holonomy
Dominic Joyce
- 01 Jan 2000
TL;DR: The first known examples of these manifolds were discovered by the author in 1993-5 as mentioned in this paper, and much previously unpublished material which significantly improves the original constructions was presented in this book.
1.4K