5,636 research outputs found
An Application of the Moving Frame Method to Integral Geometry in the Heisenberg Group
We show the fundamental theorems of curves and surfaces in the 3-dimensional
Heisenberg group and find a complete set of invariants for curves and surfaces
respectively. The proofs are based on Cartan's method of moving frames and Lie
group theory. As an application of the main theorems, a Crofton-type formula is
proved in terms of p-area which naturally arises from the variation of volume.
The application makes a connection between CR geometry and integral geometry
Harmonic and quasi-harmonic spheres, part III. Rectifiablity of the parabolic defect measure and generalized varifold flows
We study weakly convergent sequences of suitable weak solutions of heat flows of harmonic maps or approximated harmonic maps. We prove a dimensional stratification for the space-time concentration measure and verify that the concentration measure, viewed as a generalized varifold, moves according to the generalized varifold flow rule which reduces to the Brakke’s flow of varifold provided that the limiting harmonic map flow is suitable. We also establish an energy quantization for the density of the limiting varifold
Finslerian MOND versus the Strong Gravitational Lensing of the Early-type Galaxies
The gravitational lensing of Bullet Clusters and early-type galaxies pose
serious challenges on the validity of MOND. Recently, Finslerian MOND, a
generalization of MOND in the framework of Finsler gravity, has been proposed
to explain the mass discrepancy problem of Bullet Cluster 1E 0657\ 558. In this
paper, we check the validity of the Finslerian MOND in describing the strong
gravitational lensing of early-type galaxies. The investigation on ten strong
lenses of the CASTLES samples shows that there is no strong evidence for the
existence of dark matter.Comment: 11 pages, 2 figures, 2 table
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