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Supergravity as Generalised Geometry I: Type II Theories
Supergravity Generalised Geometry I High Energy Physics - Theory
2011/9/30
Abstract: We reformulate ten-dimensional type II supergravity as a generalised geometrical analogue of Einstein gravity, defined by an $O(9,1)\times O(1,9)\subset O(10,10)\times\bbR^+$ structure on th...
Schrodinger equations, deformation theory and $tt^*$-geometry
Schrodinger equations deformation theory Differential Geometry
2011/8/26
Abstract: This is the first of a series of papers to construct the deformation theory of the form Schr\"odinger equation, which is related to a section-bundle system $(M,g,f)$, where $(M,g)$ is a nonc...
Lie algebroid modules and representations up to homotopy
Lie algebroid representation up to homotopy graded manifold graded vector bundle Q-manifold
2011/8/30
Abstract: We explain how Lie algebroid modules in the sense of Vaintrob provide geometric models for Lie algebroid representations up to homotopy. Specifically, we show that there is a noncanonical wa...
Four-orbifolds with positive isotropic curvature
Ricci flow with surgery four orbifolds positive isotropic curvature
2011/8/29
Abstract: In this note we prove the following result: Let $\mathcal{O}$ be a compact, connected Riemannian 4-orbifold with singular set of codimension at least 2 and with positive isotropic curvature....
Mass-capacity inequalities for conformally flat manifolds with boundary
Mass-capacity inequalities conformally flat manifolds boundary
2011/8/29
Abstract: In this paper we prove a mass-capacity inequality and a volumetric Penrose inequality for conformally flat manifolds, in arbitrary dimensions. As a by-product of the proofs, capacity and Ale...
On osp(p+1,q+1|2r)-equivariant quantizations
Orthosymplectic algebra Differential operator Equivariant quantization Casimir operators
2011/8/29
Abstract: We investigate the concept of equivariant quantization over the superspace R^{p+q|2r}, with respect to the orthosymplectic algebra osp(p+1,q+1|2r). Our methods and results vary upon the supe...
Spectral and stochastic properties of the $f$-Laplacian, solutions of PDE's at infinity, and geometric applications
Weighted Laplacians Feller property stochastic completeness essential spectrum gradient Ricci solitons
2011/8/26
Abstract: The aim of this paper is to suggest a new viewpoint to study qualitative properties of solutions of semilinear elliptic PDE's defined outside a compact set. The relevant tools come from spec...
Equivariant inverse spectral theory and toric orbifolds
Laplacian symplectic orbifold toric moment polytope equivariant spectrum constant scalar curvature
2011/8/25
Abstract: Let O be a symplectic toric 2n-dimensional orbifold with a fixed T^n-action and with a toric Kahler metric g. We previously explored whether, when O is a manifold, the equivariant spectrum o...
On supersymmetric Einstein-Weyl spaces
supersymmetric Einstein-Weyl spaces High Energy Physics - Theory Differential Geometry
2011/9/29
Abstract: We use techniques developed for the classification of supersymmetric solutions to find Einstein-Weyl metrics with Lorentzian signature in arbitrary dimensions. We find that all supersymmetri...
Special Lagrangian 4-folds with $SO(2)\rtimes S_3$-Symmetry in Complex Space Forms
Lagrangian 4-folds Complex Space Forms Differential Geometry
2011/8/25
Abstract: In this article we obtain a classification of special Lagrangian submanifolds in complex space forms subject to an $SO(2)\rtimes S_3$-symmetry on the second fundamental form. The algebraic s...
Long time existence of the symplectic mean curvature flow
symplectic mean curvature flow Long time Differential Geometry
2011/8/25
Abstract: Let $(M,\bar{g})$ be a K\"ahler surface with a constant holomorphic sectional curvature $k>0$, and $\Sigma$ an immersed symplectic surface in $M$. Suppose $\Sigma$ evolves along the mean cur...
Abstract: Let R be an o-minimal expansion of the real field. We introduce a class of Hausdorff limits, the T-infinity limits over R, that do not in general fall under the scope of Marker and Steinhorn...
Abstract: For $(M,[g])$ a conformal manifold of signature $(p,q)$ and dimension at least three, the conformal holonomy group $\mathrm{Hol}(M,[g]) \subset O(p+1,q+1)$ is an invariant induced by the can...
How to produce a Ricci Flow via Cheeger-Gromoll exhaustion
Ricci Flow Cheeger-Gromoll exhaustion Differential Geometry
2011/8/24
Abstract: We prove short time existence for the Ricci flow on open manifolds of nonnegative complex sectional curvature. We do not require upper curvature bounds. By considering the doubling of convex...
The geometry of embedded pseudo-Riemannian surfaces in terms of Poisson brackets
pseudo-Riemannian manifolds embedded surfaces Poisson brackets
2011/8/25
Abstract: Arnlind, Hoppe and Huisken showed how to express the Gauss and mean curvature of a surface embedded in a Riemannian manifold in terms of Poisson brackets of the embedding coordinates. We gen...