Metric minimizing surfaces

Metric Minimizing Surfaces

Consider a two-dimensional surface in an Alexandrov space of curvature bounded above by k. Assume that this surface does not admit contracting deformations (a particular case of such surfaces is formed by area minimizing surfaces). Then this surface inherits the upper curvature bound, that is, this surface has also curvature bounded above by k, with respect to the intrinsic metric induced from ...

Minimizing light reflection from dielectric textured surfaces.

In this paper, we consider antireflective properties of textured surfaces for all texture size-to-wavelength ratios. Existence and location of the global reflection minimum with respect to geometrical parameters of the texture is a subject of our study. We also investigate asymptotic behavior of the reflection with the change of the texture geometry for the long and short wavelength limits. As ...

Are ghost surfaces quadratic-flux-minimizing?

Two candidates for “almost-invariant” toroidal surfaces passing through magnetic islands, namely quadratic-flux-minimizing (QFMin) surfaces and ghost surfaces, use families of periodic pseudo-orbits (i.e. paths for which the action is not exactly extremal). QFMin pseudo-orbits, which are coordinate-dependent, are field lines obtained from a modified magnetic field, and ghost-surface pseudo-orbi...

Optimal Lp-Metric for Minimizing Powered Deviations in Regression

Slim-Trees: High Performance Metric Trees Minimizing Overlap Between Nodes

In this paper we present the Slim-tree, a dynamic tree for organizing metric datasets in pages of fixed size. The Slim-tree uses the "fat-factor" which provides a simple way to quantify the degree of overlap between the nodes in a metric tree. It is well-known that the degree of overlap directly affects the query performance of index structures. There are many suggestions to reduce overlap in m...