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Liouville-type theorems and applications to geometry on complete Riemannian manifolds
Liouville-type theorems geometry complete Riemannian manifolds
2010/11/11
On a complete Riemannian manifold M with Ricci curvature satisfying $$\textrm{Ric}(\nabla r,\nabla r) \geq -Ar^2(\log r)^2(\log(\log r))^2...(\log^{k}r)^2$$ for $r\gg 1$, where A>0 is a constant, and ...
We use the "pearl" machinery in our previous work to study certain enumerative invariants associated to monotone Lagrangian submanifolds.
Tetrad gravity, electroweak geometry and conformal symmetry
Tetrad gravity 2-spinors electroweak geometry conformal symmetry dilaton
2010/12/3
A partly original description of gauge fields and electroweak geometry is proposed. A discussion of the breaking of conformal symmetry and the nature of the dilaton in the proposed setting indicates t...
We survey recent developments in the Birational Anabelian Geometry program aimed at the reconstruction of function fields of algebraic varieties over algebraically closed fields from pieces of their a...
By refining the Bochner formulas for any Hermitian complex vector bundle with an arbitrary metric connection over a compact Hermitian manifold, we can kill torsion and derive various vanishing theore...
We study the holomorphic unitary representations of the Jacobi group based on Siegel-Jacobi domains. Explicit polynomial orthonormal bases of the Fock spaces based on the Siegel-Jacobi disk are obtain...
Lectures on Holomorphic Curves in Symplectic and Contact Geometry
Holomorphic Curves Symplectic Contact Geometry
2010/11/12
This is a set of expository lecture notes created originally for a graduate course on holomorphic curves taught at ETH Zurich and the Humboldt University Berlin in 2009/2010. The notes are still incom...
Geometry of the Banach spaces C(beta mathbb N times K, l_p) for compact metric spaces K
Geometry of the Banach spaces C compact metric spaces K
2010/11/19
In this paper we provide the complete isomorphic classification of the spaces C(beta mathbb N times K, l_p) of all continuous l_p-valued functions, 1 <= p < infinity, defined on the topological produ...
Quaternionic Grassmannians and Pontryagin classes in algebraic geometry
Quaternionic Grassmannians Pontryagin classes algebraic geometry
2010/11/9
The quaternionic Grassmannian HGr(r,n) is the affine open subscheme of the ordinary Grassmannian parametrizing those 2r-dimensional subspaces of a 2n-dimensional symplectic vector space on which the ...
Short loop decompositions of surfaces and the geometry of Jacobians
Short loop decompositions the geometry of Jacobians
2010/11/19
Given a Riemannian surface, we consider a naturally embedded graph which captures part of the topology and geometry of the surface. By studying this graph, we obtain results in three different directi...
Modifications of Hodge bundles and enumerative geometry : the stable hyperelliptic locus. Part 1: semicompact type
Hodge bundles enumerative geometry stable hyperelliptic locus
2010/11/9
We compute, in terms of tautological classes, the fundamental class of the locus of stable hyperelliptic curves, i.e. the closure in the moduli space of stable curves of the locus of smooth hyperellip...
Five lectures on optimal transportation: Geometry, regularity and applications
optimal transportation Geometry regularity applications
2010/11/19
In this series of lectures we introduce the Monge-Kantorovich problem of optimally transporting one distribution of mass onto another, where optimality is measured against a cost function c(x,y). Con...
On Explicit Holmes-Thompson Area Formula in Integral Geometry
Minkowski space Holmes-Thompson Volume symplectic structure
2010/12/13
In this article, we give an exposition on the Holmes-Thompson theory developed by Alvarez. The space of geodesics in Minkowski space has a symplectic structure which is induced by the projection from ...
Construction of schemes over $F_1$, and over idempotent rings: towards tropical geometry
$F_1$ over idempotent rings towards tropical geometry
2010/11/26
In this paper, we give some categorical description of the general spectrum functor, defining it as an adjoint of a global section functor.The general spectrum functor includes that of F1 and of semir...
Geometry of Topological Defects of Two-dimensional Sigma Models
Geometry of Topological Defects Two-dimensional Sigma Models
2010/12/16
A topological defect separating a pair of two-dimensional CFTs is a codimension one interface along which all components of the stress-energy tensor glue continuously. We study topological defects of ...