By Ali Baklouti, Aziz El Kacimi, Sadok Kallel, Nordine Mir
This e-book contains 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 complicated variables, who kicked the bucket in 2011. All study articles have been written through top specialists, a few of whom are prize winners within the fields of advanced geometry, algebraic geometry and research. The booklet deals a precious source for all researchers drawn to fresh advancements in research and geometry.
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Additional info for Analysis and Geometry: MIMS-GGTM, Tunis, Tunisia, March 2014. In Honour of Mohammed Salah Baouendi
Z|2 We obtain (10c). Another way to obtain (10c) uses the symmetry of interchanging the variables, a unitary change in the domain. Consider the map (z, w) → (z 2 , w) = h(z, w). On the sphere, we have |z|4 + |w|2 = ||h(z, w)||2 = ||h(w, z)||2 = |w|4 + |z|2 . (13) Dividing both sides of (13) by |z|2 and moving the | wz |2 term over yields (10c). We could have divided instead by |w|2 and found an equivalent map. More interesting is to divide by |z|4 . Then we obtain the map 2 1 2 w , z, w z2 from Lebl’s list , which (by ) is also equivalent to (10c).
12 Let C be an annulus of R2N included in the set ξ ∈ R2N / |ξ| > 1 . For any nonnegative integer k, there exist positive constants Ck and Ck so that, for any real number p ≥ 1 and any function u belonging to L p (R2N ) satisfying Supp u ⊂ eλ C , with λ ≥ 1, we have C k λk u L p (R2N ) ≤ (log |D|)k u L p (R2N ) ≤ C k λk u L p (R2N ) . 8 is more challenging. The result we obtain in the logarithmic frame reads differently from that of the classical case, but expresses the same phenomenon, namely that we lose 2N 1p − q1 derivatives in the passage from the L p norm to the L q norm, for q ≥ p ≥ 1.
X. Huang, S. Ji, Mapping Bn into B2n−1 . Inventiones Mathematicae 145, 219–250 (2001) 19. S. Ji, Y. Zhang, Classification of rational holomorphic maps from B 2 into B N with degree 2. Sci. China Ser. A 52, 2647–2667 (2009) 20. L. Lempert, Imbedding Cauchy-Riemann manifolds into a sphere. Int. J. Math. 1, 91–108 (1990) 21. J. Lebl, Normal forms, Hermitian operators, and CR maps of spheres and hyperquadrics. Michigan Math. J. 60(3), 603–628 (2011) 22. J. Lebl, H. Peters, Polynomials constant on a hyperplane and CR maps of spheres.
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