We study the existence of geometrically controlled branched covering maps from R to open 3-manifolds or to decomposition spaces S/G, and from S/G to S. Dedicated to the memory of Fred Gehring, whose work has been our inspiration

ABSTRACT There is a growing interest in utilizing intrinsic alignment (IA) of galaxy shapes as geometric and dynamical probe cosmology. In this paper, we present the first measurements IA modified gravity model using gravitational shear-intrinsic ellipticity correlation (GI) ellipticity-ellipticity (II) functions dark-matter haloes from f(R) simulations. By comparing them with same statistics m...

Abstract We provide a general approach to Lipschitz regularity of solutions for large class vector-valued, nonautonomous variational problems exhibiting nonuniform ellipticity. The functionals considered here range from those with unbalanced polynomial growth conditions fast, exponential type growth. results obtained are sharp respect all the data and also yield new, optimal criteria in classic...

We consider the problem of an elliptical background source crossing a linear gravitational lensing fold caustic. We derive a simple expression for the light curve of a source with a uniform surface brightness that is accurate to third order in the ellipticity e (yielding brightness errors of . 1% for e . 0.3). We then consider caustic crossings of a rotating star, an oblate giant extrasolar pla...

We investigate the orientation correlation of giant elliptical galaxies by measuring the intrinsic ellipticity correlation function of 83,773 luminous red galaxies (LRGs) at redshifts 0.16 – 0.47 from the Sloan Digital Sky Survey. We have accurately determined the correlation up to 30 h Mpc. Luminosity dependence of the ellipticity correlation is also detected although the error bars are large,...