Related Experiment Video
Updated: Aug 9, 2026

Applying an eMASS Customization Program as a Research Tool to Evaluate Consumer Benefits
Published on: September 27, 2019
On completeness of the Bergman metric and its subordinate metric
1Department of Mathematics, The Pennsylvania State University, University Park, Pa. 16802.
Abstract:
It is proved that on any bounded domain in the complex Euclidean space C(n) the Bergman metric is always greater than or equal to the Carathéodory distance. This leads to a number of interesting consequences. Here two such consequences are given. (i) The Bergman metric is complete whenever the Carathéodory distance is complete on a bounded domain. (ii) The Weil-Petersson metric is not uniformly equivalent to the Bergman metric in the Teichmüller space T(g) of any Riemann surface of genus g >/= 2.
Related Concept Videos
Routh-Hurwitz Criterion II
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first column of the Routh...
Routh-Hurwitz Criterion I
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
Degree of Curvature and Radius of Curvature
Relating Angular And Linear Quantities - II
Moment-Area Theorems
The theorem is divided into two parts. The first part connects the angle between tangents at any two points on the beam's elastic curve to the area under a curve derived by plotting...
Dot Product of Two Vectors
