Sphere-preserving maps in inversive geometry
نویسندگان
چکیده
منابع مشابه
Sphere-preserving Maps in Inversive Geometry
We give an extensive discussion of sphere-preserving maps defined on subdomains of Euclidean n-space, and their relationship to Möbius maps and to the preservation of cross-ratios. In the case n = 2 (the complex plane) we also relate these ideas to the solutions of certain functional equations.
متن کاملWhat is inversive geometry?
Suppose ↵, are concentric. Let a and b denote the radii of ↵ and respectively, and assume a > b. Clearly, such an arrangement of circles i exists only when the centers C1, . . . , Cn of the n circles 1, . . . n are the vertices of a regular n-gon, whose center is the common center O of ↵ and . Consider then a point of tangency T between two circles i and i+1, and the triangle 4OCiT . The edge O...
متن کاملLinear maps preserving or strongly preserving majorization on matrices
For $A,Bin M_{nm},$ we say that $A$ is left matrix majorized (resp. left matrix submajorized) by $B$ and write $Aprec_{ell}B$ (resp. $Aprec_{ell s}B$), if $A=RB$ for some $ntimes n$ row stochastic (resp. row substochastic) matrix $R.$ Moreover, we define the relation $sim_{ell s} $ on $M_{nm}$ as follows: $Asim_{ell s} B$ if $Aprec_{ell s} Bprec_{ell s} A.$ This paper characterizes all linear p...
متن کاملInterior fixed points of unit-sphere-preserving Euclidean maps
Schirmer proved that there is a class of smooth self-maps of the unit sphere in Euclidean n-space with the property that any smooth self-map of the unit ball that extends a map of that class must have at least one fixed point in the interior of the ball. We generalize Schirmer’s result by proving that a smooth self-map of Euclidean n-space that extends a self-map of the unit sphere of that clas...
متن کاملOn strongly Jordan zero-product preserving maps
In this paper, we give a characterization of strongly Jordan zero-product preserving maps on normed algebras as a generalization of Jordan zero-product preserving maps. In this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly Jordan zero-product preserving maps are completely different. Also, we prove that the direct p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2001
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-01-06427-9