Search results for "Variable"
showing 10 items of 1674 documents
Nonexistence of Quasiconformal Maps Between Certain Metric Measure Spaces
2013
We provide new conditions that ensure that two metric measure spaces are not quasiconformally equivalent. As an application, we deduce that there exists no quasiconformal map between the sub-Riemannian Heisenberg and roto-translation groups.
Characterizing boundedness of metaplectic Toeplitz operators
2023
We study Toeplitz operators on the Bargmann space, with Toeplitz symbols given by exponentials of complex quadratic forms. We show that the boundedness of the corresponding Weyl symbols is necessary for the boundedness of the operators, thereby completing the proof of the Berger-Coburn conjecture in this case. We also show that the compactness of such Toeplitz operators is equivalent to the vanishing of their Weyl symbols at infinity.
Bohr radii of vector valued holomorphic functions
2012
Abstract Motivated by the scalar case we study Bohr radii of the N -dimensional polydisc D N for holomorphic functions defined on D N with values in Banach spaces.
Numerical study of the transverse stability of the Peregrine solution
2020
We generalise a previously published approach based on a multi-domain spectral method on the whole real line in two ways: firstly, a fully explicit 4th order method for the time integration, based on a splitting scheme and an implicit Runge--Kutta method for the linear part, is presented. Secondly, the 1D code is combined with a Fourier spectral method in the transverse variable both for elliptic and hyperbolic NLS equations. As an example we study the transverse stability of the Peregrine solution, an exact solution to the one dimensional nonlinear Schr\"odinger (NLS) equation and thus a $y$-independent solution to the 2D NLS. It is shown that the Peregrine solution is unstable against all…
The Riemann hypothesis : the great pending mayhematical challenge
2018
The Riemann hypothesis is an unproven statement referring to the zeros of the Riemann zeta function. Bernhard Riemann calculated the first six non-trivial zeros of the function and observed that they were all on the same straight line. In a report published in 1859, Riemann stated that this might very well be a general fact. The Riemann hypothesis claims that all non-trivial zeros of the zeta function are on the the line x=1/2. The more than ten billion zeroes calculated to date, all of them lying on the critical line, coincide with Riemann?s suspicion, but no one has yet been able to prove that the zeta function does not have non-trivial zeroes outside of this line.
Sobolev estimates for optimal transport maps on Gaussian spaces
2012
We will study variations in Sobolev spaces of optimal transport maps with the standard Gaussian measure as the reference measure. Some dimension free inequalities will be obtained. As application, we construct solutions to Monge-Ampere equations in finite dimension, as well as on the Wiener space.
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 …
A symmetrization result for Monge–Ampère type equations
2007
In this paper we prove some comparison results for Monge–Ampere type equations in dimension two. We also consider the case of eigenfunctions and we derive a kind of “reverse” inequalities. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Kähler Tubes of Constant Radial Holomorphic Sectional Curvature
1997
We determine (up to holomorphic isometries) the family of Kahler tubes, around totally geodesic complex submanifolds, of constant radial holomorphic sectional curvature when the centreP of the tube is either simply connected or a complex hypersurface withH1 (P, R)=0. In the last case, these tubes have the topology of tubular neighbourhoods of the zero section of the complex lines bundles over symplectic manifolds (when they are Kahler) of the Kostant-Souriau prequantization.
Semiclassical Gevrey operators and magnetic translations
2020
We study semiclassical Gevrey pseudodifferential operators acting on the Bargmann space of entire functions with quadratic exponential weights. Using some ideas of the time frequency analysis, we show that such operators are uniformly bounded on a natural scale of exponentially weighted spaces of holomorphic functions, provided that the Gevrey index is $\geq 2$.