An immersion of manifolds is a map with everywhere injective differential. Two immersions are regularly homotopic if there exists a continuous 1–parameter family of immersions connecting one to the other. The Smale–Hirsch h–principle [8, 4] says that the space of immersions M → N , dim(M) < dim(N) is homotopy equivalent to the space of injective bundle maps TM → TN . In contrast to differential...

This paper proposes an automatic segmentation method of vessel walls that combines an implicit 3D model of the vessels and a total curvature penalizer in a level set evolution scheme. First, the lumen is segmented by alternating a model-guided level set evolution and a recalculation of the model itself. Second, the level set of the lumen is evolved with a term that aims at penalizing the total ...

This paper proves that classical minimal surfaces of arbitrary topological type with total boundary curvature at most 4 must be smoothly embedded. Related results are proved for varifolds and for soap lm surfaces. In a celebrated paper N3] of 1973, Nitsche proved that if ? is an analytic simple closed curve in R 3 with total curvature at most 4, then ? bounds exactly one minimal disk M. Further...

introduction: complete knowledge of root canal curvature is a critical factor in successful dental treatment .the aim of this study was to investigate the direction, radius and degree of curvature of maxillary anterior teeth and the relation between radius and degree of curvature in babol city. methods &materials;: this study was performed on 242 anterior teeth radiographs were taken by periapi...

The index of a metric plays significant roles in differential geometry as it generates variety of vector fields such as space-like, time-like, and light-like fileds. With the help of these vector fields, we establish interesting properties on ( )-Sasakian manifolds, which was introduced by Bejancu and Duggal [1] and further investigated by Xufeng and Xiaoli [2]. Since Sasakian manifolds with in...

We prove that a sequence of, possibly branched, weak immersions of the two-sphere S into an arbitrary compact riemannian manifold (M, h) with uniformly bounded area and uniformly bounded L−norm of the second fundamental form either collapse to a point or weakly converges as current, modulo extraction of a subsequence, to a Lipschitz mapping of S and whose image is made of a connected union of f...

We classify complete nonorientable minimal surfaces in R3 with total curvature −8π.

to evaluate the effect of application of municipal solid waste compost (mswc) on the accumulation of heavy metals of lead, nickel and cadmium in the soil under maize cultivation, a factorial experiment in base randomized complete block design (rcbd) with four different amounts of municipal solid waste compost (zero, 15, 30 and 60 tons ha-1) and time (compost applied once or twice) was performed...