Convex Combinations of Minimal Graphs
نویسندگان
چکیده
منابع مشابه
Convex Combinations of Minimal Graphs
Given a collection of minimal graphs,M1,M2, . . . ,Mn, with isothermal parametrizations in terms of the Gauss map and height differential, we give sufficient conditions onM1,M2, . . . ,Mn so that a convex combination of themwill be a minimal graph. We will then provide two examples, taking a convex combination of Scherk’s doubly periodic surface with the catenoid and Enneper’s surface, respecti...
متن کاملMinimal Graphs in R over Convex Domains
Krust established that all conjugate and associate surfaces of a minimal graph over a convex domain are also graphs. Using a convolution theorem from the theory of harmonic univalent mappings, we generalize Krust’s theorem to include the family of convolution surfaces which are generated by taking the Hadamard product or convolution of mappings. Since this convolution involves convex univalent ...
متن کاملConvex combinations of harmonic shears of slit mappings
In this paper, we study the convex combinations of harmonic mappings obtained by shearing a class of slit conformal mappings. Sufficient conditions for the convex combinations of harmonic mappings of this family to be univalent and convex in the horizontal direction are derived. Several examples of univalent harmonic mappings constructed by using these methods are presented to illustrate...
متن کاملConvex Sets and Convex Combinations
Convexity is one of the most important concepts in a study of analysis. Especially, it has been applied around the optimization problem widely. Our purpose is to define the concept of convexity of a set on Mizar, and to develop the generalities of convex analysis. The construction of this article is as follows: Convexity of the set is defined in the section 1. The section 2 gives the definition...
متن کاملConvex sets in graphs, II. Minimal path convexity
A set K of vertices in a connected graph is M-convex if and only if for every pair of vertices in K, all vertices of all chordless paths joining them also lie in K. Carathtodory, Helly and Radon type theorems are proved for M-convex sets. The Caratheodory number is 1 for complete graphs and 2 for other graphs, The Helly number equals the size of a maximum clique. The Radon number is one more th...
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: International Journal of Mathematics and Mathematical Sciences
سال: 2012
ISSN: 0161-1712,1687-0425
DOI: 10.1155/2012/724268