to be isothermal.) Isothermal coordinates on surfaces were first introduced by Gauss. Korn and Lichtenstein proved that isothermal coordinates exist around...

the mathematical field of differential geometry, the existence of isothermal coordinates for a (pseudo-)Riemannian metric is often of interest. In the case...

coordinate system given by f is isothermal. Conversely, consider a diffeomorphism f that does give us isothermal coordinates. We then have μ ( z ) = ( u x...

dimensions, certain harmonic coordinates known as isothermal coordinates have been studied since the early 1800s. Harmonic coordinates in higher dimensions were...

(\log r),} where r denotes the geodesic distance from the point. In isothermal coordinates, first considered by Gauss, the metric is required to be of the...

equation appears in the study of isothermal coordinates in differential geometry: the independent variables x,y are the coordinates, while f can be described...

existence of a canonical form is equivalent to the existence of isothermal coordinates for the associated Riemannian metric A ( x , y ) d x 2 + 2 B ( x...

spacetime)#Proper coordinates or Fermi coordinates Geodesic normal coordinates Fermi–Walker transport Christoffel symbols Isothermal coordinates Manasse, F....

linearly independent, so that u and v give local isothermal coordinates. The existence of isothermal coordinates can be proved by other methods, for example...

used the later-named Beltrami equation to prove the existence of isothermal coordinates on analytic surfaces. The essay concludes with examples of conformal...

manifold is conformally flat, a consequence of the existence of isothermal coordinates. Indeed, the existence of a conformally flat scale amounts to solving...

surface. This can be seen as a consequence of the existence of isothermal coordinates. In complex analytic terms, the Poincaré–Koebe uniformization theorem...

conformal, i.e. scale the metric by a smooth function. The existence of isothermal coordinates—which can be proved using either local existence theorems for the...

curvature is Liouville's equation in terms of the Laplacian in isothermal coordinates. The surface integral of the Gaussian curvature over some region...

applications in medical image analysis, computer vision and graphics. Isothermal coordinates Quasiregular map Pseudoanalytic function Teichmüller space Tissot's...

horizon, and y A {\displaystyle y^{A}} are isothermal coordinates on the horizon. Remark: In Gaussian null coordinates, the black hole horizon corresponds to...

horocycle in the appropriate Q quadrant. For example, in thermodynamics the isothermal process explicitly follows the hyperbolic path and work can be interpreted...

Riemann surface in a canonical way; this is known as the existence of isothermal coordinates. Conversely, every Riemann surface is Kähler since the Kähler form...

}}_{u}=S_{u}^{2}} (as shown in ref., complex stereographic rather than real isothermal coordinates are used just for the convenience of completely solving NP equations)...

fundamental form is sufficiently small. By using the Codazzi equation and isothermal coordinates, they also obtained rigidity results on two-dimensional closed submanifolds...

case of two-dimensional surfaces, making use of the existence of isothermal coordinates. Slightly weaker estimates were obtained by Schoen and Simon, although...

Figur der Himmelskörper. 1922, Reprint: VDM, Saarbrücken 2007. Isothermal coordinates Symmetrizable compact operator Murnaghan, F. D. (1930). "Review:...

The isothermal–isobaric ensemble (constant temperature and constant pressure ensemble) is a statistical mechanical ensemble that maintains constant temperature...

1869 by Massieu for the isothermal process (both quantities differs just with a figure sign) and by then Planck for the isothermal-isobaric process. More...

z } {\displaystyle \{y,z\}} are either real isothermal coordinates or complex stereographic coordinates labeling the cross-sections of { v=constant,...

third depicted the locus of the isothermal chromaticities on the CIE 1931 x,y chromaticity diagram. Since the isothermal points formed normals on his UCS...

Isothermal Community College (ICC) is a public community college in Spindale, North Carolina. Named after its location in the thermal belt, an area in...

general circulation models and numerical weather prediction Singular isothermal sphere profile Lambda-CDM model, the standard model of Big Bang cosmology...

space; that is, a color is specified by a set of three numbers (the CIE coordinates X, Y, and Z, for example, or other values such as hue, colorfulness,...

the theory of partial differential equations by the use of curvilinear coordinates, and the mathematical theory of elasticity (for which linear elasticity...