By Friedrich Hirzebruch, Shiing-Shen Chern

The Wei-Liang Chow and Kuo-Tsai Chen Memorial convention was once proposed and held via Professor S.-S. Chern. It used to be dedicated to memorializing these remarkable and unique mathematicians who had made major contributions to algebraic geometry and algebraic topology, respectively. It additionally supplied a discussion board for top mathematicians to expound and talk about their perspectives on new principles in those fields, in addition to tendencies in 21st-century arithmetic. approximately a hundred mathematicians participated within the convention, together with Sir Michael Atiyah, Jacob Palis, Phillip Griffiths, David Eisenbud, Philippe Tondeur, Yujiro Kawamata, Tian Gang, and others. This quantity includes chosen papers awarded on the convention. the subjects contain canonical maps of Gorenstein three-folds, primary teams of algebraic curves, Chen's interated integrals, algebraic fibre areas, and extra Lars V. Ahlfors / F. W. Gehring -- Ahlfors' Preface to his amassed Papers 7 -- Caratheodory's document on Ahlfors' paintings for the Fields Medal on the ICM in Oslo 1936 eleven -- Ahlfors' tackle as Honorary President on the establishing of the ICM in Berkeley 1986 14 -- An Extension of Schwarz's Lemma 15 -- Quasiconformal Reflections 21 -- Finitely Generated Kleinian teams 32 -- Henri Cartan -- Breve examine des travaux fifty one -- Les Seminaires Cartan (allocution prononcee par J.-P. Serre en 1975) sixty two -- Varietes analytiques complexes et cohomologie sixty seven -- Espaces fibres et groupes d'homotopie. I. structures generales / J.-P. Serre eighty two -- Espaces fibres et groupes d'homotopie. II. functions / J.-P. Serre eighty five -- Discours prononce le ler fevrier 1977 a l'occasion de l. a. remise de l. a. Medaille d'Or du C.N.R.S. 88 -- Lennart A. E. Carleson -- Lennart Carleson's paintings in research / P. W. Jones ninety six -- Lennart Carleson's paintings in Statistical Mechanics and Dynamical platforms / M. Benedicks 108 -- On Convergence and development of Partial Sums of Fourier sequence one hundred twenty -- Shiing-Shen Chern -- My Mathematical schooling 154 -- S. S. Chern as Geometer and good friend / A. Weil 169 -- Abzahlungen fur Gewebe 173 -- an easy Intrinsic facts of the Gauss-Bonnet formulation for Closed Riemannian Manifolds 181 -- On Finsler Geometry 187 -- Ennio De Giorgi / M. Miranda -- Ennio de Giorgi (1928-1996) / J.-L. Lions, F. Murat 192 -- De Giorgi's summer season vacation trips and XIX Hilbert challenge / M. Miranda 206 -- Alcune applicazioni al Calcolo delle variazioni di una teoria della misura K-dimensionale 207 -- minimum Cones and the Bernstein challenge / E. Bombieri, E. Giusti 208 -- New difficulties in [Gamma]-convergence and G-convergence 234 -- Samuel Eilenberg / W. S. Massey -- Samuel Eilenberg (1913-1998) / H. Bass, H. Cartan, P. Freyd, A. Heller, S. MacLane 242 -- ordinary Isomorphisms in team thought / S. MacLane 256 -- Singular Homology thought 263 -- Axiomatic method of Homology thought / N. E. Steenrod 288 -- Paul Erdos / B. Bollobas -- The lifestyles and paintings of Paul Erdos / B. Bollobas 292 -- chosen guides of Paul Erdos 316 -- The Gaussian legislations of mistakes within the conception of Additive quantity Theoretic capabilities / M. Kac 328 -- The manufactured from Consecutive Integers isn't an influence / J. L. Selfridge 333 -- Friedrich Hirzebruch -- Bibliography after 1987 344 -- Curriculum vitae mathematicae / H. Grauert, G. more durable, R. Remmert 345 -- Friedrich Hirzebruch -- An Appreciation / M. F. Atiyah 347 -- On Steenrod's diminished Powers, The Index of Inertia, and the Todd Genus 352 -- mathematics Genera and the concept of Riemann-Roch for Algebraic forms 358 -- Riemann-Roch Theorems for Differentiable Manifolds / M. F. Atiyah 363 -- studying complicated research in Munster-Paris, Zurich and Princeton from 1945 to 1953 369 -- Kunihiko Kodaira: Mathematician, pal, and instructor 382 -- Wolf Prize rite The Knesset 389 -- beginning Speech, ICM Berlin 1998 390 -- Lars Hormander -- My Mathematical schooling 404 -- at the thought of basic Partial Differential Operators 410 -- Differential Equations with out suggestions 500 -- Hypoelliptic moment Order Differential Equations 505 -- Kiyosi Ito -- Foreword in Kiyosi Ito: chosen Papers 531 -- On a formulation referring to Stochastic Differentials 540 -- a number of Wiener critical 551 -- The Brownian movement and Tensor Fields on Riemannian Manifold 564 -- Stochastic Differentials 568 -- Joseph B. Keller -- Biographical comic strip 578 -- ebook checklist 579 -- Geometrical idea of Diffraction 599 -- Corrected Bohr-Sommerfeld Quantum stipulations for Nonseparable structures 614 -- Kunihiko Kodaira / Y. Miyaoka, ok. Ueno -- lifetime of Kunihiko Kodaira / Y. Miyaoka, okay. Ueno 623 -- On a Differential-Geometric procedure within the idea of Analytic Stacks 653 -- On Compact Analytic Surfaces 659 -- Robert Langlands -- difficulties within the idea of Automorphic kinds 679 -- Jean Leray / P. Malliavin -- Jean Leray Works / P. Malliavin 706 -- Biographie de Jean Leray / P. Malliavin 709 -- Sur le mouvement d'un fluide visqueux emplissant l'espace (introduction merely) 711 -- Topologie et equations fonctionnelles / J. Schauder 715 -- Sur un probleme de illustration conforme pose par los angeles theorie de Helmholtz / A. Weinstein 718 -- L'anneau d'homologie d'une illustration 721 -- constitution de l'anneau d'homologie d'une illustration 724 -- Proprietes de l'anneau d'homologie de l. a. projection d'un espace fibre sur sa base 727 -- choice, dans les cas non exceptionnels, de l'anneau de cohomologie de l'espace homogene quotient d'un groupe de Lie compact par un sous-groupe de meme rang 730 -- Prolongement de los angeles transformation de Laplace 733 -- l. a. theorie des residus sur une variete analytique complexe 741 -- l. a. calcul differentiel et crucial sur une variete analytique complexe 746 -- Systeme d'equations aux derivees partielles a caracteristiques multiples: probleme de Cauchy ramifie; hyperbolicite partielle (introduction purely) / Y. Hamada, C. Wagschal 753 -- Prolongements analytiques de los angeles resolution du probleme de Cauchy lineaire (introduction in simple terms) / Y. Hamada, A. Takeuchi 756

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14 QUASIOOHrOBMAL MIXECTIOXS 301 References [1). L. ABLroits & L. Baas, Rietnenn's mapping theorem for variable metrics. Ann. of Math. 72 (I960). 385-404. [2]. L. AHLTOBS A. A. BKURUNO, The boundary correspondence under quasiconformal map­ ping*. , 96 (19S6), 125-142. [3]. L. AHLTOU k G. VVaux, A uniqueness theorem for Beltrami equationa. Proc. Amtr. Math. Soc.. 13 (1962). 975-978. (4). L. B i l l (to appear). [5]. , Correction to "Spaces of Riemann surfaces as bounded domains". Butt. Amtr. Math.

Soit G(a) le groupe d'isotropie d'un point a e D, c'est-a-dire le sous-groupe forme des automorphis­ mes qui laissent fixe le point a. Un premier resultat est le suivant: l'application qui, a chaque element de G (a), associe la transformation lineaire tangente en a, est un isomorphisme de G (a) sur un sous-groupe (compact) du groupe lineaire GL(n,C). J'ai prouve cela a partir d'un lemme tres simple, qui dit que si une transformation holomorphe /de D dans D (non supposee bijective) laisse fixe un point a e D et est tangente a l'identite en a, c'est l'application identique.

We choose agaia **(•) — a V ^ l —*£)-« and obtain *(C)—0, contrary to assumption. 6. There is a generalisation of Lemma 5 which will be of importance when we pass to the case of Eleinian groups. Let 0 , be an arbitrary subgroup of 0. B(G). It is to be observed that the first inner product is orer D/0, the second orer D/G+ Larnti 6. Every +£Q(G) eon be vriiU* at «*, vith «%€ Q(G,). *, TV> — 0 for all *. € Q(G). 11) thk gives <** I"»*> — 0 for all «s* and hence «\>—0, a contradiction. 6. The general case.

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