Bøger i Memoirs of the American Mathematical Society serien

The authors consider a category of pairs of compact metric spaces and Lipschitz maps where the pairs satisfy a linearly isoperimetric condition related to the solvability of the Plateau problem with partially free boundary. It includes properly all pairs of compact Lipschitz neighbourhood retracts of a large class of Banach spaces.

The authors establish square function estimates for integral operators on uniformly rectifiable sets by proving a local $T(b)$ theorem and applying it to show that such estimates are stable under the so-called big pieces functor. More generally, they consider integral operators associated with Ahlfors-David regular sets of arbitrary codimension in ambient quasi-metric spaces.

Introduces the reader to global Carleman estimates for a class of parabolic operators which may degenerate at the boundary of the space domain, in the normal direction to the boundary. Such a kind of degeneracy is relevant to study the invariance of a domain with respect to a given stochastic diffusion flow, and appears naturally in climatology models.

Let $G$ be a simple classical algebraic group over an algebraically closed field $K$ of characteristic $p \ge 0$ with natural module $W$. Let $H$ be a closed subgroup of $G$ and let $V$ be a non-trivial irreducible tensor-indecomposable $p$-restricted rational $KG$-module such that the restriction of $V$ to $H$ is irreducible. In this paper the authors classify the triples $(G,H,V)$ of this form.

Examines the following singularly perturbed problem: - 2 ?u V(x)u=f(u) in R N . Their main result is the existence of a family of solutions with peaks that cluster near a local maximum of V(x). A local variational and deformation argument in an infinite dimensional space is developed to establish the existence of such a family for a general class of nonlinearities f .

Sets up a language to deal with Dirac operators on manifolds with corners of arbitrary co-dimension. This book develops a theory of boundary reductions, introducing the notion of a taming of a Dirac operator as an invertible perturbation by a smoothing operator.

Explores ramifications and extensions of a $q$-difference operator method first used by L J Rogers for deriving relationships between special functions involving certain fundamental $q$-symmetric polynomials. This work also presents expansions of certain generalized basic hypergeometric functions in terms of the symmetric polynomials.

The aim of this work is to adapt the complex analytic methods originating in modern Oka theory to the study of non-orientable conformal minimal surfaces in $\mathbb{R}^n$ for any $n\ge 3$.

The authors characterize the affine spaces in terms of the combinatorics of a fixed coefficient quiver for $M$. The method of proof is to exhibit explicit equations for the Schubert cells of $\mathrm{Gr}_{\underline{e}}(M)$ and to solve this system of equations successively in linear terms.

Let $G$ be a reductive group over the field $F=k((t))$, where $k$ is an algebraic closure of a finite field, and let $W$ be the (extended) affine Weyl group of $G$. The associated affine Deligne-Lusztig varieties $X_x(b)$, which are indexed by elements $b \in G(F)$ and $x \in W$, were introduced by Rapoport.

Using the new versions of the abstract band method, we solve the positive extension problem for almost periodic matrix functions of several real variables with Fourier coefficients indexed in a given additive subgroup of the space of variables.

Following the method developed by Waldspurger and Beuzart-Plessis in their proofs of the local Gan-Gross-Prasad conjecture, the author is able to prove the geometric side of a local relative trace formula for the Ginzburg-Rallis model.

This work is devoted to the study of rates of convergence of the empirical measures $\mu_{n} = \frac {1}{n} \sum_{k=1}^n \delta_{X_k}$, $n \geq 1$, over a sample $(X_{k})_{k \geq 1}$ of independent identically distributed real-valued random variables towards the common distribution $\mu$ in Kantorovich transport distances $W_p$.

The normal matrix model with algebraic potential has gained a lot of attention recently, partially in virtue of its connection to several other topics as quadrature domains, inverse potential problems and the Laplacian growth. In this volume the authors consider the normal matrix model with cubic plus linear potential.

The authors develop a theory of $THH$ and $TC$ of Waldhausen categories and prove the analogues of Waldhausen's theorems for $K$-theory. They resolve the longstanding confusion about localization sequences in $THH$ and $TC$, and establish a specialized devissage theorem.

Two of the central concepts for the study of degree structures in computability theory are computably enumerable degrees and minimal degrees. This book considers how minimal weak truth table degrees interact with computably enumerable Turing degrees and obtain three main results.

The main idea of this article is to carry out a Lubin-Tate generalization of the theory of cyclotomic $(\varphi,\Gamma )$-modules in a different fashion. Instead of the $p$-adic open unit disk, the authors work over a character variety that parameterizes the locally $L$-analytic characters on $o_L$.

Presents generalization of Szemeredi's Regularity Lemma to a certain hypergraph setting.

Introduces and studies the bounded word problem and the precise word problem for groups given by means of generators and defining relations. The main technical result of the paper states that, for certain finite presentations of groups the bounded word problem and the precise word problem can be solved in polylogarithmic space.

Develops a decomposition theory for subgroups of $\mathsf{Out}(F_n)$ which generalizes the decomposition theory for individual elements of $\mathsf{Out}(F_n)$ found in the work of Bestvina, Feighn, and Handel, and which is analogous to the decomposition theory for subgroups of mapping class groups found in the work of Ivanov.

The author considers semilinear parabolic equations of the form $u_t=u_xx f(u),\quad x\in \mathbb R,t>0,$ where $f$ a $C^1$ function. Assuming that $0$ and $\gamma >0$ are constant steady states, the author investigates the large-time behavior of the front-like solutions.

In this paper, the authors prove global well-posedness of the massless Maxwell-Dirac equation in the Coulomb gauge on $\mathbb{R}^{1+d} (d\geq 4)$ for data with small scale-critical Sobolev norm, as well as modified scattering of the solutions.

Presents a detailed analysis of 2-complete stable homotopy groups, both in the classical context and in the motivic context over $\mathbb C$. The author uses the motivic May spectral sequence to compute the cohomology of the motivic Steenrod algebra over $\mathbb C$ through the 70-stem.

The authors construct cornered Floer homology invariants of 3-manifolds with codimension-2 corners and prove that the bordered Floer homology of a 3-manifold with boundary, split into two pieces with corners, can be recovered as a tensor product of the cornered invariants of the pieces.

The main object of this work is to present a powerful method of construction of subshifts which the authors use chiefly to construct WAP systems with various properties. Among many other applications of these so-called labeled subshifts, the authors obtain examples of null as well as non-null WAP subshifts.

Explains the foundations of a version of algebraic geometry in which rings or algebras are replaced by $C^\infty $-rings. As schemes are the basic objects in algebraic geometry, the new basic objects are $C^\infty $-schemes, a category of geometric objects which generalize manifolds and whose morphisms generalize smooth maps.

In 1925 Elie Cartan introduced the principal of triality specifically for the Lie groups of type $D_4$, and in 1935 Ruth Moufang initiated the study of Moufang loops. The observation of the title in 1978 was made by Stephen Doro, who was motivated by George Glauberman. Here the author makes the statement precise in a categorical context.