Geometry of compact lifting spaces

The Geometry of Compact Homogeneous Spaces with Two Isotropy Summands

We give a complete list of all homogeneous spaces M = G/H where G is a simple compact Lie group, H a connected, closed subgroup, and G/H is simply connected, for which the isotropy representation of H on TpM decomposes into exactly two irreducible summands. For each homogeneous space, we determine whether it admits a G-invariant Einstein metric. When there is an intermediate subgroup H < K < G,...

Compact Symmetric Spaces, Triangular Factorization, and Poisson Geometry

LetX be a simply connected compact Riemannian symmetric space, let U be the universal covering group of the identity component of the isometry group of X , and let g denote the complexification of the Lie algebra of U , g = u. Each u-compatible triangular decomposition g = n − + h + n+ determines a Poisson Lie group structure πU on U . The Evens-Lu construction ([EL]) produces a (U, πU )-homoge...

Selection of Suitable Geometry in Compact Heat Exchanger Design

Lifting in Sobolev Spaces

for some function φ : Ω → R. The objective is to find a lifting φ “as regular as u permits.” For example, if u is continuous one may choose φ to be continuous and if u ∈ C one may also choose φ to be C. A more delicate result asserts that if u ∈ VMO (= vanishing means oscillation), then one may choose φ to be also VMO (see R. Coifman and Y. Meyer [1] and H. Brezis and L. Nirenberg [1]). In this...

Complexity Spaces: Lifting & Directedness

The theory of complexity spaces has been introduced in [Sch95] as part of the development of a topological foundation for Complexity Analysis. The topological study of these spaces has been continued in the context of the theory of upper weightable spaces ([Sch96]), while the specific properties of total boundedness and Smyth completeness have been analyzed in [RS96]. Here we introduce a techni...