Results 31 to 40 of about 257,471 (64)
Subquadratic harmonic functions on Calabi‐Yau manifolds with maximal volume growth
Communications on Pure and Applied Mathematics, Volume 77, Issue 6, Page 3080-3106, June 2024.Abstract On a complete Calabi‐Yau manifold M$M$ with maximal volume growth, a harmonic function with subquadratic polynomial growth is the real part of a holomorphic function. This generalizes a result of Conlon‐Hein. We prove this result by proving a Liouville‐type theorem for harmonic 1‐forms, which follows from a new local L2$L^2$ estimate of the ...
Shih‐Kai Chiu
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Evanescent ergosurfaces and ambipolar hyperkähler metrics [PDF]
, 2016 A bstractA supersymmetric solution of 5d supergravity may admit an ‘evanescent ergosurface’: a timelike hypersurface such that the canonical Killing vector field is timelike everywhere except on this hypersurface.
Benjamin E. Niehoff, H. Reall
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Gravitational instantons with quadratic volume growth
Journal of the London Mathematical Society, Volume 109, Issue 4, April 2024.Abstract There are two known classes of gravitational instantons with quadratic volume growth at infinity, known as type ALG$\operatorname{ALG}$ and ALG∗$\operatorname{ALG}^*$. Gravitational instantons of type ALG$\operatorname{ALG}$ were previously classified by Chen–Chen.
Gao Chen, Jeff Viaclovsky
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Limits of Riemannian 4‐manifolds and the symplectic geometry of their twistor spaces
Transactions of the London Mathematical Society, Volume 4, Issue 1, Page 100-109, December 2017., 2017 Abstract The twistor space of a Riemannian 4‐manifold carries two almost complex structures, J+ and J−, and a natural closed 2‐form ω. This article studies limits of manifolds for which ω tames either J+ or J−. This amounts to a curvature inequality involving self‐dual Weyl curvature and Ricci curvature, and which is satisfied, for example, by all anti‐
Joel Fine
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Closed 3‐forms in five dimensions and embedding problems
Journal of the London Mathematical Society, Volume 109, Issue 4, April 2024.Abstract We consider the question if a five‐dimensional manifold can be embedded into a Calabi–Yau manifold of complex dimension 3 such that the real part of the holomorphic volume form induces a given closed 3‐form on the 5‐manifold. We define an open set of 3‐forms in dimension five which we call strongly pseudoconvex, and show that for closed ...
Simon Donaldson, Fabian Lehmann
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Integrability of Einstein deformations and desingularizations
Communications on Pure and Applied Mathematics, Volume 77, Issue 1, Page 177-220, January 2024.Abstract We study the question of the integrability of Einstein deformations and relate it to the question of the desingularization of Einstein metrics. Our main application is a negative answer to the long‐standing question of whether or not every Einstein 4‐orbifold (which is an Einstein metric space in a synthetic sense) is limit of smooth Einstein ...
Tristan Ozuch
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One‐dimensional local families of complex K3 surfaces
Bulletin of the London Mathematical Society, Volume 56, Issue 1, Page 296-305, January 2024.Abstract For any complex K3 surface X$X$, we construct a one‐dimensional deformation in which all integers ρ$\rho$ with 0⩽ρ⩽20$0 \leqslant \rho \leqslant 20$ occur as Picard numbers of some fibres. In contrast, we prove that the generic one‐dimensional local family of K3 surfaces admits only 0 and 1 as Picard numbers of the fibres.
Riccardo Carini, Francesco Viganò
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A note on the Kähler and Mori cones of hyperkähler manifolds
, 2015 In the present paper we prove that, on a hyperkähler manifold, walls of the Kähler cone and extremal rays of the Mori cone are determined by all divisors satisfying certain numerical conditions.
Giovanni Mongardi
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The Looijenga-Lunts-Verbitsky Algebra and Verbitsky's Theorem. [PDF]
Milan J Math, 2022 Bottini A.
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