John域

本文研究了Ｊｏｈｎ域，证明了有界一致域必定是Ｊｏｈｎ域和Ｊｏｈｎ域是拟共形不变量．     

John Leslie Britton

John Leslie Britton died in a climbing accident on the Isleof Skye on 13 June 1994 at the age of 66. He became a memberof the London Mathematical Society in 1957, served the societyas Meetings and Membership Secretary from 1973 to 1976, andat the same time was Editor of the Society's Newsletter.     

Generalized John disks

We establish the basic properties of the class of generalized simply connected John domains.     

John Frank Adams

Frank Adams was born in Woolwich on 5 November 1930. His homewas in New Eltham, about ten miles east of the centre of London.Both his parents were graduates of King's College, London, whichwas where they had met. They had one other child — Frank'syounger brother Michael — who rose to the rank of AirVice-Marshal in the Royal Air Force. In his creative gifts and practical sense, Frank took afterhis father, a civil engineer, who worked for the governmenton road building in peace-time and airfield construction inwar-time. In his exceptional capacity for hard work, Frank tookafter his mother, who was a biologist active in the educationalfield.     

Julia and John

Using a recent result of Mañé [Ma] we give a classification of polynomials whose Fatou components are John domains.Supported in part by NSF Grant DMS-8916968     

John and Loewner Ellipsoids

John’s ellipsoid criterion characterizes the unique ellipsoid of globally maximum volume contained in a given convex body C. In this article local and global maximum properties of the volume on the space of all ellipsoids in C are studied, where ultra maximality is a stronger version of maximality: the volume is nowhere stationary. The ellipsoids for which the volume is locally maximum, resp. locally ultra maximum are characterized. The global maximum is the only local maximum and for generic C it is an ultra maximum. The characterizations make use of notions originating from the geometric theory of positive quadratic forms. Part of these results generalize to the case where the ellipsoids are replaced by affine copies of a convex body D. In contrast to the ellipsoid case, there are convex bodies C and D, such that on the space of all affine images of D in C the volume has countably many local maxima. All results have dual counterparts. Extensions to the surface area and, more generally, to intrinsic volumes are mentioned.     

The logarithmic John ellipsoid

The logarithmic John ellipsoid of a convex body in \({\mathbb {R}}^{n}\) with its centroid at the origin is introduced by solving a pair of dual optimization problems. Convex bodies with identical John and logarithmic John ellipsoids are characterized.     

Unions of John domains

We study the question: When is the union of John domains a John domain?