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Quantitative Stratification and the Regularity of Harmonic Maps and Minimal Currents
Quantitative Stratification the Regularity of Harmonic Maps Minimal Currents
2011/9/9
Abstract: We introduce techniques for turning estimates on the infinitesimal behavior of solutions to nonlinear equations (statements concerning tangent cones and blow ups) into more effective control...
Transitive Lie algebras of vector fields---an overview
Transitive Lie algebras vector fields Differential Geometry
2011/9/6
Abstract: This overview paper is intended as a quick introduction to Lie algebras of vector fields. Originally introduced in the late 19th century by Sophus Lie to capture symmetries of ordinary diffe...
Some geometric analysis on generic Ricci solitons
Ricci solitons X–Laplacian scalar curvature estimates maximum principles volume estimates
2011/9/6
Abstract: We study the geometry of complete generic Ricci solitons with the aid of some geometric-analytical tools extending techniques of the usual Riemannian setting.
Co--calibrated $G_2$ structure from cuspidal cubics
cuspidal cubics Differential Geometry Algebraic Geometry
2011/9/6
Abstract: We establish a twistor correspondence between a cuspidal cubic curve in a complex projective plane, and a co-calibrated homogeneous $G_2$ structure on the seven--dimensional parameter space ...
Equidistribution of Eisenstein series on convex co-compact hyperbolic manifolds
Equidistribution of Eisenstein series convex co-compact hyperbolic manifolds Spectral Theory
2011/9/5
Abstract: For convex co-compact hyperbolic manifolds $\Gamma\backslash \mathbb{H}^{n+1}$ for which the dimension of the limit set satisfies $\delta_\Gamma< n/2$, we show that the high-frequency Eisens...
On smoothness of isometries between orbit spaces
Isometric groups action singular Riemannian foliations invariant function basic form
2011/9/5
Abstract: We discuss the connection between the smooth and metric structure on quotient spaces, prove smoothness of isometries in special cases and discuss an application to a conjecture of Molino.
Optimal paths for symmetric actions in the unitary group
geodesic segment Lagrangian optimal path unitarily invariant norm unitary group Grassmann manifold angular metric
2011/9/5
Abstract: Given a positive and unitarily invariant Lagrangian L defined in the algebra of Hermitian matrices, and a fixed interval $[a,b]\subset\mathbb R$, we study the action defined in the Lie group...
Abstract: The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The 3-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetime...
A geometric heat flow for vector fields
Geometric heat flow Killing vector fields Yano’s theorem Navier-Stokes equations
2011/9/6
Abstract: This is an announcement of our work [5] on introducing and studying a geometric heat flow to find Killing vector fields on closed Riemannian manifolds with positive sectional curvature. We s...
The complex Goldberg-Sachs theorem in higher dimensions
The complex Goldberg-Sachs theorem higher dimensions Differential Geometry
2011/9/2
Abstract: We study the geometric properties of holomorphic distributions of totally null $m$-planes on a $(2m+\epsilon)$-dimensional complex Riemannian manifold $(\mathcal{M}, \bm{g})$, where $\epsilo...
The Local Product Theorem for bihamiltonian structures
The Local Product Theorem bihamiltonian structures Symplectic Geometry Differential Geometry
2011/9/2
Abstract: In this work one proves that, around each point of a dense open set (regular points), a real analytic or holomorphic bihamiltonian structure decomposes into a product of a Kronecker bihamilt...
On one class of holonomy groups in pseudo-Riemannian geometry
holonomy groups pseudo-Riemannian geometry Differential Geometry
2011/9/5
Abstract: We prove the following theorem. Let g be a nondegenerate bilinear form on a vector space V, and L:V -> V a g-symmetric operator. Then the centraliser of L in SO(g) is a holonomy group for a ...
Estimates on the modulus of expansion for vector fields solving nonlinear equations
Estimates vector fields nonlinear equations Differential Geometry
2011/9/5
Abstract: By adapting methods of \cite{AC} we prove a sharp estimate on the expansion modulus of the gradient of the log of the parabolic kernel to the Sch\"ordinger operator with convex potential, wh...
The Kahler-Ricci flow on projective bundles
The Kahler-Ricci flow projective bundles Differential Geometry
2011/9/1
Abstract: We study the behaviour of the K\"ahler-Ricci flow on projective bundles. We show that if the initial metric is in a suitable K\"ahler class, then the fibers collapse in finite time and the m...
Abstract: We propose a formulation of a Lorentzian quantum geometry based on the framework of causal fermion systems. After giving the general definition of causal fermion systems, we deduce space-tim...