terracing is an operator that is applied to potential field data to produce regions of constant field amplitude that are separated by sharp boundaries. magnetic data are usually transformed into pseudo-gravity data (baranov, 1957) prior to the application of terracing. the objective of terracing is ‘to recast potential field maps into a geologic map like format’ (cordell and mccafferty 1989). t...

Curvature formulas for implicit curves and surfaces are derived from the classical curvature formulas in Differential Geometry for parametric curves and surfaces. These closed formulas include curvature for implicit planar curves, curvature and torsion for implicit space curves, and mean and Gaussian curvature for implicit surfaces. Some extensions of these curvature formulas to higher dimensio...

The flag curvature is a natural extension of the sectional curvature in Riemannian geometry, and the S-curvature is a non-Riemannian quantity which vanishes for Riemannian metrics. There are (incomplete) nonRiemannian Finsler metrics on an open subset in Rn with negative flag curvature and constant S-curvature. In this paper, we are going to show a global rigidity theorem that every Finsler met...

We study various transport-information inequalities under three di erent notions of Ricci curvature in the discrete setting: the curvature-dimension condition of Bakry and Émery [4], the exponential curvature-dimension condition of Bauer et al. [6] and the coarse Ricci curvature of Ollivier [38]. We prove that under a curvature-dimension condition or coarse Ricci curvature condition, an L1 tran...

The relationship between the orientation and curvature of projected curves and the orientation and curvature of the underlying space curve has been previously established. This has allowed a disambiguation of correspondences in two views and a transfer of these properties to a third view for confirmation. We propose that a higher-order intrinsic differential geometry attribute, namely, curvatur...

We consider the graphical mean curvature flow of strictly area decreasing maps $f:M\to N$, where $M$ is a compact Riemannian manifold dimension $m>1$ and $N$ complete surface bounded geometry. prove long-time existence that property preserved, when bi-Ricci $BRic_M$ from below by sectional $\sigma_N$ $N$. In addition, we obtain smooth convergence to minimal map if $Ric_M\ge\sup\{0,{\sup}_N\sigm...

We prove that the total curvature of any planar graph with nonnegative combinatorial is an integral multiple 1 12 \frac {1}{12} </mml:se...

We study the properties of $n$-volumic scalar curvature in this note. Lott-Sturm-Villani's curvature-dimension condition ${\rm CD}(\kappa,n)$ was showed to imply Gromov's $\geq n\kappa$ under an additional $n$-dimensional and we show stability \kappa$ with respect smGH-convergence. Then propose a new weighted on Riemannian manifold its properties.