Some Extremal Questions for Simplicial Complexes. V: The Relative Area of a Klein Bottle
Abstract
This final note of the series indicates how greatly we still lack information, not only as to some of the most basic facts in the higher Euclidean spaces, but also as to the question whether these facts, and even other much better known facts, are perhaps completely irrelevant in problems of analysis. This last question is further complicated by the partly Cartesian character of the underlying space in certain contexts: in fluid dynamics this space is not Euclidean, it is at best a Cartesian product of Euclidean, or locally Euclidean, spaces, corresponding to the highly dissimilar sets of variables, which specify the position, pressure, and thermo-dynamic or electro-magnetic state. One striking, and certainly basic, fact in higher Euclidean spaces, is the familiar existence of a Klein bottle. It has had, so far, no very noticeable effect in the problems of classical analysis. We shall be concerned, however, with an example in least area, which exhibits in this respect a small but significant effect. We discuss its scope as far as our methods allow, and we indicate, as a challenge to the reader, the very wide range of possibilities that are left open.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 01, 1962
- Accession Number
- AD0299226
Entities
People
- L. C. Young
Organizations
- University of Wisconsin–Madison