Results 31 to 40 of about 257,471 (64)
Subquadratic harmonic functions on Calabi‐Yau manifolds with maximal volume growth
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
wiley +1 more source
Evanescent ergosurfaces and ambipolar hyperkähler metrics [PDF]
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
semanticscholar +1 more source
Gravitational instantons with quadratic volume growth
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
wiley +1 more source
Limits of Riemannian 4‐manifolds and the symplectic geometry of their twistor spaces
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
wiley +1 more source
Closed 3‐forms in five dimensions and embedding problems
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
wiley +1 more source
Integrability of Einstein deformations and desingularizations
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
wiley +1 more source
One‐dimensional local families of complex K3 surfaces
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
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
semanticscholar +1 more source
The Looijenga-Lunts-Verbitsky Algebra and Verbitsky's Theorem. [PDF]
Bottini A.
europepmc +1 more source