In the past few decades, the quantitative computation of surface roughness has received increasing attention due to its importance in numerical surface study. In this paper, concepts of mathematical morphology are employed to compute and characterize the surface roughness of catchments extracted from a simulated digital elevation model (DEM). Morphological smoothing is implemented on the simula...

In 1956, Shiffman [Sh] proved that any compact minimal annulus with two convex boundary curves (resp. circles) in parallel planes is foliated by convex planar curves (resp. circles) in the intermediate planes. In 1978, Meeks conjectured that the assumption the minimal surface is an annulus is unnecessary [M]; that is, he conjectured that any compact connected minimal surface with two planar con...

\ due. Several existing algorithms are available for solving the convex problem (6). We refer to a recent paper by Boyd and Yang [4. Sect. ;] discussing the details, including the advantages and disadvantages, of [hese numerical algorithms. AS a result. if W(a) is convex (which is alwavs the case when m < 3; see [51, for example), cl (~)(=c( (a)) could be computed with any of these algorithms. ...

The deviation of a general convex body with twice differentiable boundary and an arbitrarily positioned polytope given number vertices is studied. paper considers the case where measured in terms surface areas involved sets, more precisely, by what called area deviation. proof uses arguments constructions from probability, integral geometry. bound closely related to p-affine areas.