Search results for "manifold"
showing 10 items of 415 documents
A rigidity theorem for the pair ${\cal q}{\Bbb C} P^n$ (complex hyperquadric, complex projective space)
1999
Given a compact Kahler manifold M of real dimension 2n, let P be either a compact complex hypersurface of M or a compact totally real submanifold of dimension n. Let \(\cal q\) (resp. \({\Bbb R} P^n\)) be the complex hyperquadric (resp. the totally geodesic real projective space) in the complex projective space \({\Bbb C} P^n\) of constant holomorphic sectional curvature 4\( \lambda \). We prove that if the Ricci and some (n-1)-Ricci curvatures of M (and, when P is complex, the mean absolute curvature of P) are bounded from below by some special constants and volume (P) / volume (M) \(\leq \) volume (\(\cal q\))/ volume \(({\Bbb C} P^n)\) (resp. \(\leq \) volume \(({\Bbb R} P^n)\) / volume …
Norm, essential norm and weak compactness of weighted composition operators between dual Banach spaces of analytic functions
2017
Abstract In this paper we estimate the norm and the essential norm of weighted composition operators from a large class of – non-necessarily reflexive – Banach spaces of analytic functions on the open unit disk into weighted type Banach spaces of analytic functions and Bloch type spaces. We also show the equivalence of compactness and weak compactness of weighted composition operators from these weighted type spaces into a class of Banach spaces of analytic functions, that includes a large family of conformally invariant spaces like BMOA and analytic Besov spaces.
Universal infinitesimal Hilbertianity of sub-Riemannian manifolds
2019
We prove that sub-Riemannian manifolds are infinitesimally Hilbertian (i.e., the associated Sobolev space is Hilbert) when equipped with an arbitrary Radon measure. The result follows from an embedding of metric derivations into the space of square-integrable sections of the horizontal bundle, which we obtain on all weighted sub-Finsler manifolds. As an intermediate tool, of independent interest, we show that any sub-Finsler distance can be monotonically approximated from below by Finsler ones. All the results are obtained in the general setting of possibly rank-varying structures.
On Słowikowski, Raíkov and De Wilde Closed Graph Theorems
1986
Publisher Summary This chapter focuses on the Slowikowski, Raikov and De Wilde closed graph theorems. The vector spaces used in the chapter, are defined over the field Ղ of real or complex numbers. The term, “space” means separated topological vector space, unless the contrary is specifically stated. If Ω is a non-empty open subset of the n -dimensional euclidean space, then the Schwartz space ҟ′(Ω) endowed with the strong topology belongs to this class. The chapter also studies the classes of spaces related with this conjecture. The class of Slowikowski spaces contains the F-spaces and it is stable with respect to the operations that include: countable topological direct sums, closed subsp…
Geometric approaches to particle physics
2008
Geometric approaches to particle physics have opened up new perspectives and unifying insights. After a few historical remarks I discuss the essence of the concept of G-theory: a primordial symmetry acting on a manifold and on the fields defined on it. This is then illustrated by the finite-dimensional case of Kaluza-Klein theories and by the infinite-dimensional case of chiral anomalies in Yang-Mills theories. In the latter case, a new and unifying description of topological and global anomalies is obtained.
Frobenius polynomials for Calabi–Yau equations
2008
We describe a variation of Dwork’ s unit-root method to determine the degree 4 Frobenius polynomial for members of a 1-modulus Calabi–Yau family over P1 in terms of the holomorphic period near a point of maximal unipotent monodromy. The method is illustrated on a couple of examples from the list [3]. For singular points, we find that the Frobenius polynomial splits in a product of two linear factors and a quadratic part 1− apT + p3T 2. We identify weight 4 modular forms which reproduce the ap as Fourier coefficients.
SPECTRAL GEOMETRY OF SPACETIME
2000
Spacetime, understood as a globally hyperbolic manifold, may be characterized by spectral data using a 3+1 splitting into space and time, a description of space by spectral triples and by employing causal relationships, as proposed earlier. Here, it is proposed to use the Hadamard condition of quantum field theory as a smoothness principle.
Total curvatures of compact complex submanifolds in $$C/P^n$$
1995
LetM be a complex submanifold in\(C/P^n\). We define the total curvatures ofM and we get a local interpretation of them. Finally, we give a topological characterization for the total (non-absolute) curvature of complex hypersurfaces in\(C/P^n\).
Hydraulic assessment of an upgraded pipework arrangement for the DEMO divertor plasma facing components cooling circuit
2021
Abstract In the context of the Work Package DIVertor (WPDIV) of the EUROfusion action, a research campaign has been carried out by University of Palermo in cooperation with ENEA to assess the thermal-hydraulic performances of the DEMO divertor cooling system, concentrating the attention on its 2019 Plasma Facing Components (PFCs) configuration, relevant to DEMO baseline 2017. The research activity has been performed following a theoretical-numerical technique based on the finite volume method and adopting the well-known ANSYS CFX CFD code. The PFCs cooling circuit thermal-hydraulic performances under nominal steady-state conditions, assessed mainly in terms of coolant total pressure drop, c…
Differentiability of the isoperimetric profile and topology of analytic Riemannian manifolds
2012
Abstract We show that smooth isoperimetric profiles are exceptional for real analytic Riemannian manifolds. For instance, under some extra assumptions, this can happen only on topological spheres. To cite this article: R. Grimaldi et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009).