By Ali Baklouti, Aziz El Kacimi, Sadok Kallel, Nordine Mir
This ebook comprises chosen papers provided on the MIMS (Mediterranean Institute for the Mathematical Sciences) - GGTM (Geometry and Topology Grouping for the Maghreb) convention, held in reminiscence of Mohammed Salah Baouendi, a most famed determine within the box of a number of advanced variables, who passed on to the great beyond in 2011. All learn articles have been written by means of best specialists, a few of whom are prize winners within the fields of advanced geometry, algebraic geometry and research. The booklet bargains a precious source for all researchers attracted to contemporary advancements in research and geometry.
Read or Download Analysis and Geometry: MIMS-GGTM, Tunis, Tunisia, March 2014. In Honour of Mohammed Salah Baouendi PDF
Best differential geometry books
This ebook is set the graceful type of a undeniable category of algebraicsurfaces, specifically normal elliptic surfaces of geometric genus one, i. e. elliptic surfaces with b1 = zero and b2+ = three. The authors provide a entire class of those surfaces as much as diffeomorphism. They accomplish that outcome via in part computing considered one of Donalson's polynomial invariants.
This quantity includes the complaints of a convention held in Cagliari, Italy, from September 7-10, 2009, to have a good time John C. Wood's sixtieth birthday. those papers mirror the numerous features of the speculation of harmonic maps and its hyperlinks and connections with different subject matters in Differential and Riemannian Geometry.
The winding quantity is without doubt one of the most simple invariants in topology. It measures the variety of instances a relocating element $P$ is going round a hard and fast element $Q$, only if $P$ travels on a direction that by no means is going via $Q$ and that the ultimate place of $P$ is equal to its beginning place. this straightforward concept has far-reaching purposes.
- The Geometry of Supermanifolds (Mathematics and Its Applications)
- The Geometry of Submanifolds
- Quantum Geometry: A Framework for Quantum General Relativity
- Differential and physical geometry
- Differential Geometry of Curves and Surfaces
Additional info for Analysis and Geometry: MIMS-GGTM, Tunis, Tunisia, March 2014. In Honour of Mohammed Salah Baouendi
1) The space L(R2N ) it will be question in this paper is the Orlicz space associated to 2 the function φ(s) = es − 1. 2 u where β N = S2N −1 . 2) 2N π 2N 22N 2 πN , with ω2N −1 = the measure of the unit sphere ω2N −1 (N − 1)! 3) whose lack of compactness has been investigated by several authors (for further details, we refer to [7, 9, 12, 21, 22, 27]). -L. 3) in 2D is due to two reasons. The first reason is the lack of compactness at infinity that can be illustrated by the sequence u n (x) = ϕ(x + xn ), where 0 = ϕ ∈ D and |xn | → ∞, and the second reason is of concentration-type and can be highlighted by the example by Moser (see [21–23]) defined by: f αn (x) = ⎧ ⎪ ⎨ αn 2π log |x| √ − ⎪ 2αn π ⎩ 0 if |x| ≤ e−αn , if if e−αn ≤ |x| ≤ 1, |x| ≥ 1, Logarithmic Littlewood-Paley Decomposition and Applications to Orlicz Spaces 37 where α := (αn ) is a sequence of positive real numbers going to infinity.
12. Taking advantage of the fact that the spectrum of the function u is included in eλ C with λ ≥ 1, we find that u(ξ) = φ(λ−1 log |ξ|) u(ξ), where φ is a function of D(R) chosen as above. Therefore (log |D|)k u = (log |D|)k gλ u , where gλ (ξ) = φ(λ−1 log |ξ|). 7) Obviously F((log |D|)k gλ )(ξ) = λk (λ−1 log |ξ|)k φ(λ−1 log |ξ|) , thus in view of the relation 1 1 1 = − + 1 , our purpose is to establish that the r q p function gk,λ (x) := (2π)−2N R2N ei x·ξ φk (λ−1 log |ξ|) dξ 1 with φk (ρ) = ρk φ(ρ), satisfies gk,λ L r (R2N ) e2N λ b (1− r ) .
3, we state and establish some logarithmic Sobolev embeddings that occur in Orlicz spaces. We mention that the letter C will be used to denote an absolute constant which may vary from line to line. We also use A B to denote an estimate of the form A ≤ C B for some absolute constant C. 48 H. Bahouri 2 Proof of Bernstein Inequalities This section is devoted to the proof of Bernstein inequalities in the framework of the logarithmic Littlewood-Paley decomposition. Adapting these fundamental inequalities provides various functional inequalities such as Sobolev embeddings and their refined versions.
Analysis and Geometry: MIMS-GGTM, Tunis, Tunisia, March 2014. In Honour of Mohammed Salah Baouendi by Ali Baklouti, Aziz El Kacimi, Sadok Kallel, Nordine Mir