We prove that a Ricci curvature based method of triangulation of compact Riemannian manifolds, due to Grove and Petersen, extends to the context of weighted Riemannian manifolds and more general metric measure spaces. In both cases the role of the lower bound on Ricci curvature is replaced by the curvature-dimension condition CD(K,N). We show also that for weighted Riemannian manifolds the tria...

dually flat finsler metrics form a special and valuable class of finsler metrics in finsler information geometry,which play a very important role in studying flat finsler information structure. in this paper, we prove that everylocally dually flat generalized randers metric with isotropic s-curvature is locally minkowskian.

BACKGROUND The purpose of this study was to assess the effectiveness of 2% ethylenediaminetetraacetic acid (EDTA) for the treatment of band-shaped keratopathy. METHODS We studied 24 eyes of 16 patients with band-shaped keratopathy who underwent EDTA chelation treatment from April 1, 2011 to December 31, 2012. We compared preoperative and 1 month postoperative logarithm of the minimum angle of...

In this paper, by modifying Cheng-Yau$'$s technique to complete hypersurfaces in $S^{n+1}(1)$, we prove a rigidity theorem under the hypothesis of the mean curvature and the normalized scalar curvature being linearly related which improve the result of [H. Li, Hypersurfaces with constant scalar curvature in space forms, {em Math. Ann.} {305} (1996), 665--672].  

We establish some relative volume comparison theorems for extremal volume forms of‎ ‎Finsler manifolds under suitable curvature bounds‎. ‎As their applications‎, ‎we obtain some results on curvature and topology of Finsler manifolds‎. ‎Our results remove the usual assumption on S-curvature that is needed in the literature‎.

As the first step in the direction of the Hopf conjecture on the non-existence of metrics with positive sectional curvature on S2 × S2 the authors of [GT] suggested the following (Weak Hopf) conjecture (on the rigidity of non-negatively curved metrics on S2 × R3): ”The boundary S2 × S2 of the S2 × B3 ⊂ S2 × R3 with an arbitrary complete metric of non-negative sectional curvature contains a poin...

Humans manipulate objects chiefly within their lower visual field, a consequence of upright posture and the anatomical position of hands and arms.This study tested the hypothesis of enhanced sensitivity to a range of stimuli within the lower visual field. Following current models of hierarchical processing within the ventral steam, discrimination sensitivity was measured for orientation, curvat...

We consider the horizontal plane at eye height, that is all objects seen at the horizon. Although this plane visually degenerates into a line in the visual field, the 'depth' dimension nevertheless gives it a two-dimensional structure. We address the problem of intrinsic curvature of this plane. The classical geometric method is based on Gauss's original definition: The angular excess in a tria...