By P Li, Gang Tian, Shiu-Yuen Cheng
This quantity is a set of analysis papers on nonlinear partial differential equations and comparable components, representing many elements of latest advancements in those components. specifically, the next are incorporated: nonlinear conservation legislation; semilinear elliptic equations, nonlinear hyperbolic equations; nonlinear parabolic equations; singular restrict difficulties; and research of actual and numerical strategies. vital parts comparable to numerical research, rest concept, multiphase thought, kinetic thought, combustion conception, dynamical structures and quantum box thought also are coated The existence and arithmetic of Shiing-Shen Chern / R.S. Palais and C.-L. Terng -- My Mathematical schooling / S.S. Chern -- A precis of My clinical existence and Works / S.S. Chern -- S.S. Chern as Geometer and good friend / A. Weil -- a few Reflections at the Mathematical Contributions of S.S. Chern / P.A. Griffiths -- Shiing-Shen Chern as good friend and Mathematician / W.-L. Chow -- Abzahlungen fur Gewebe -- On crucial Geometry in Klein areas -- an easy Intrinsic evidence of the Gauss-Bonnet formulation for Closed Riemannian Manifolds -- at the Curvatura Integra in a Riemannian Manifold -- attribute sessions of Hermitian Manifolds -- Sur une Classe Remarquable de Varietes dans l'espace Projectif a N Dimensions -- A Theorem on Orientable Surfaces in 4-dimensional area / S.S. Chern and E. Spanier -- at the Kinematic formulation within the Euclidean area of N Dimensions -- On a Generalization of Kahler Geometry -- at the overall Curvature of Immersed Manifolds / S.S. Chern and R.K. Lashof
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Additional resources for A mathematician and his mathematical work : selected papers of S.S. Chern
Around 1934, I began to realize the importance of global differential geometry, call~ differential geometry in the large at that time. It was generally considered to be a difficult subject, both in the mathematical breadth required and in the depth of the problems. My main inspiration carne from Wilhelm Blaschke's books on differential geometry.
Lane at the University of Chicago. J. Wilczynski in 1901 and was a natural outgrowth of projective geometry which had reigned over geometry for almost a century. I became familiar with the literature and wrote a few papers. Among them was my master's thesis on projective line geometry. Following Plucker and Klein line geometry had been a favorite topic of geometers. , line loci defined by quadratic equations in the Plucker coordinates. They have beautiful properties; a modern treatment can be found in the book of 48 3 Shiing-Shen Chern Griffiths-Harris [11 .
Soc. vol. 44, p. 601) H. Weyl made this often quoted admission: "Cartan is undoubtedly the greatest living master in differential geometry... Nevertheless I must admit that I found the book, like most of Cartan's papers, hard reading ... " Given this well-known difficulty Cartan had in communicating his more esoteric ideas, one can easily imagine that his important insights on the Equivalence Problem might have lain buried. Fortunately they were spared such a fate. Recall that Chern had spent his time at Hamburg studying the Cartan-Kahler theory of Pfaffian systems with Kahler, and immediately after Hamburg Chern spent a year in Paris continuing his study of these techniques with Cartan.
A mathematician and his mathematical work : selected papers of S.S. Chern by P Li, Gang Tian, Shiu-Yuen Cheng