Contents Introduction 119 1. Quasiregular mappings 120 2. The Beltrami equation 121 3. The Beltrami-Dirac equation 122 4. A quest for compactness 124 5. Sharp -estimates versus variational integrals 125 6. Very weak solutions 128 7. Nonlinear commutators 129 8. Jacobians and wedge products 131 9. Degree formulas 134 References 136
We prove a vanishing theorem for the cohomology of the complement of a complex hyperplane arrangement with coefficients in a complex local system. This result is compared with other vanishing theorems, and used to study Milnor fibers of line arrangements, and hypersurface arrangements.
Let M be a real-analytic submanifold of whose “microlocal” Levi form has constant rank in a neighborhood of a prescribed conormal. Then local non-solvability of the tangential ∂̅-system is proved for forms of degrees , (and 0). This phenomenon is known in the literature as “absence of the Poincaré Lemma” and was already proved in case the Levi form is non-degenerate (i.e. ). We owe its proof to [2] and [1] in the case of a hypersurface and of a higher-codimensional submanifold respectively....
We prove that for a real analytic generic submanifold of whose Levi-form has constant rank, the tangential -system is non-solvable in degrees equal to the numbers of positive and negative Levi-eigenvalues. This was already proved in [1] in case the Levi-form is non-degenerate (with non-necessarily real analytic). We refer to our forthcoming paper [7] for more extensive proofs.
Non-split almost complex supermanifolds and non-split Riemannian supermanifolds are studied. The first obstacle for a splitting is parametrized by group orbits on an infinite dimensional vector space. For almost complex structures, the existence of a splitting is equivalent to the existence of local coordinates in which the almost complex structure can be represented by a purely numerical matrix, i.e. containing no Grassmann variables. For Riemannian metrics, terms up to degree 2 are allowed in...
Si dimostra con esempi che la distanza di Hausdorff-Carathéodory fra i valori di funzioni multivoche, analitiche secondo Oka, non è subarmonica.
A classical result of Hardy and Littlewood states that if is in , 0 < p ≤ 2, of the unit disk of ℂ, then where is a positive constant depending only on p. In this paper, we provide an extension of this result to Hardy and weighted Bergman spaces in the unit ball of , and use this extension to study some related multiplier problems in .
We introduce the extended bicomplex plane 𝕋̅, its geometric model: the bicomplex Riemann sphere, and the bicomplex chordal metric that enables us to talk about convergence of sequences of bicomplex meromorphic functions. Hence the concept of normality of a family of bicomplex meromorphic functions on bicomplex domains emerges. Besides obtaining a normality criterion for such families, the bicomplex analog of the Montel theorem for meromorphic functions and the fundamental normality tests for families...
We prove some normality criteria for families of meromorphic mappings of a domain into ℂPⁿ under a condition on the inverse images of moving hypersurfaces.