Rigidity theorem of graph-directed fractals
نویسندگان
چکیده
منابع مشابه
Finitely Ramified Graph-directed Fractals, Spectral Asymptotics and the Multidimensional Renewal Theorem
We consider the class of graph-directed constructions which are connected and have the property of finite ramification. By assuming the existence of a fixed point for a certain renormalization map, it is possible to construct a Laplace operator on fractals in this class via their Dirichlet forms. Our main aim is to consider the eigenvalues of the Laplace operator and provide a formula for the s...
متن کاملSeparation Properties for Graph-Directed Self-Similar Fractals
Examples of “separation properties” for iterated function systems of similitudes include: the open set condition, the weak separation property, finite type. Alternate descriptions for these properties and relations among these properties have been worked out. Here we consider the same situation for “graph-directed” iterated function systems, and provide the definitions and proofs for that setti...
متن کاملRigidity Properties of Locally Scaling Fractals
A set has local scaling if in a neighborhood of a point the structure of the set can be mapped onto a finer scale structure of the set. These scaling transformations are compact sets of locally affine contractions (that is, contractions with uniformly α-Hölder continuous derivatives). In this setting, without the open set condition or any other assumption on the spacing of these contractions, w...
متن کاملDirected prime graph of non-commutative ring
Prime graph of a ring R is a graph whose vertex set is the whole set R any any two elements $x$ and $y$ of $R$ are adjacent in the graph if and only if $xRy = 0$ or $yRx = 0$. Prime graph of a ring is denoted by $PG(R)$. Directed prime graphs for non-commutative rings and connectivity in the graph are studied in the present paper. The diameter and girth of this graph are also studied in the pa...
متن کاملA Rigidity Theorem for Affine Kähler-Ricci Flat Graph
where (U ) is the cofactor matrix of the Hessian matrix Df of a smooth convex function f defined in a convex domain Ω ⊂ R. The PDE (1.2) is the equation for affine maximal hypersurfaces. Obviously, every solution of (1.1) is a solution of (1.2). About complete affine maximal hypersurfaces there are two famous conjectures, one is the Chern’s conjecture (see [Ch]); another is a problem raised by ...
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: Asian Journal of Mathematics
سال: 2018
ISSN: 1093-6106,1945-0036
DOI: 10.4310/ajm.2018.v22.n6.a8