2,204 research outputs found
Ricci Curvature on Alexandrov spaces and Rigidity Theorems
In this paper, we introduce a new notion for lower bounds of Ricci curvature
on Alexandrov spaces, and extend Cheeger-Gromoll splitting theorem and Cheng's
maximal diameter theorem to Alexandrov spaces under this Ricci curvature
condition.Comment: final versio
Lipschitz continuity of harmonic maps between Alexandrov spaces
In 1997, J. Jost [27] and F. H. Lin [39], independently proved that every
energy minimizing harmonic map from an Alexandrov space with curvature bounded
from below to an Alexandrov space with non-positive curvature is locally
H\"older continuous. In [39], F. H. Lin proposed a challenge problem: Can the
H\"older continuity be improved to Lipschitz continuity? J. Jost also asked a
similar problem about Lipschitz regularity of harmonic maps between singular
spaces (see Page 38 in [28]). The main theorem of this paper gives a complete
resolution to it.Comment: We remove the assumption in the previous version that the domain
space has nonnegative generalized Ricci curvature. This solves Lin's
conjecture completely. To appear in Invent. Mat
Gravitating tensor monopole in a Lorentz-violating field theory
We present a solution of the coupled Einstein and rank-two antisymmetric
tensor field equations where Lorentz symmetry is spontaneously broken, and we
discuss its observational signatures. Especially, the deflection angles have
important qualitative differences between tensor and scalar monopoles. If a
monopole were to be detected, it would be discriminated whether or not to
correspond to a tensor one. This phenomenon might open up new direction in the
search of Lorentz violation with future astrophysical observations.Comment: 5 pages, 4 figure
Evaluation of povidone-iodine applications in cataract surgery
As a routine measure to prevent intraocular inflammation, rinsing conjunctival sac with povidone-iodine(PVP-I)has been increasingly adopted in cataract surgery. It can effectively reduce the complications of cataract surgery, including endophthalmitis and corneal complications. However, PVP-I itself has certain side effects. Therefore, to achieve the best bactericidal effect and to avoid eye injury, it is necessary to find out the optimal treatment duration and concentration. This article offers a review on the latest researches worldwide in this field
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