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Nonlinear Perron-Frobenius Theory
Guides the reader through the nonlinear Perron-Frobenius theory, introducing them to recent developments and challenging open problems.
Characterizing $k$-Dimensional Universal Menger Compacta
This memoir considers only the case of compact Menger-space-manifolds. With routine changes (open covers instead of epsilonics), the results are valid for non-compact Menger-space-manifolds. Also outlined are parts of proofs for the non-compact case that are substantially different from the compact case.
Existence Theorems for Minimal Surfaces of Non-Zero Genus Spanning a Contour
We present a modern approach to the classical problem of Plateau based purely on differential geometric concepts. We not only reprove the classical results of Douglas but also develop a new geometric criterion on a given finite system of disjoint Jordan curves in three-dimensional Euclidean space which guarantees the existence of a minimal surface of a prescribed genus having these curves as boundary.
The Meromorphic Continuation and Functional Equations of Cuspidal Eisenstein Series for Maximal Cuspidal Subgroups
We carry out, in the context of an algebraic group and an arithmetic subgroup, an idea of Selberg for continuing Eisenstein series. It makes use of the theory of integral operators. The meromorphic continuation and functional equation of an Eisenstein series constructed with a cusp form on the Levi component of a rank one cuspidal subgroup are established.
Topological Triviality and Versality for Subgroups $A$ and $K$
In this paper we shall prove two theorems which together allow the infinitesimal methods of Thom and Mather in singularity theory to be applied to problems of topological equivalence of mappings.
The Oscillator Duality Correspondence for the Pair $O(2,2)$, $SP(2,{\mathbb R})$
We calculate this correspondence and show that the unitary representation of O(2, 2), are mapped to unitary representations of Sp(2, [bold]R).
Nonlinear Commutators in Interpolation Theory
Recently, Jawerth, Rochberg and Weiss have studied nonlinear maps arising from interpolation theory which satisfy commutator relationships with interpolated linear operators. Here we present a very general result of this type for rearrangement-invariant Banach function spaces.
A Multiple Disjunction Lemma for Smooth Concordance Embeddings
Requiring background in basic differential topology, this book is aimed at researchers interested in the homotopy type of spaces of smooth embeddings and spaces of diffeomorphisms. The author provides a proof of a useful connectivity estimate in the theory of concordances (or pseudo-isotopies), generalizing Morlet's result from triads to n-ads. The method of proof is a differentiable general position technique analogous to piecewise-linear sunny collapsing.
Topologies on Pseudo-Trees and Applications
A pseudo-tree is a partially ordered set such that the set of all predecessors of any element is linearly ordered. Clearly, each linearly ordered set is a pseudo-tree and pseudo-trees are, in general, much more complicated objects than chains. The aim of this paper is to develop a theory of natural order topologies on pseudo-trees which extends the theories of linearly ordered topological spaces and GO-spaces. Moreover, applications are given for some classes of continua which admit a natural ordering.
