Function Theory on Manifolds Which Possess a Pole (Lecture Notes in Mathematics, 699) 1979th Edition by R.E. Greene (PDF)

Description

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I bought this 1979 typescript by Robert Everist Greene and his PhD advisor Hung-Hsi Wu at University of Kentucky Bookshop in 1986 for USD 17. It is a somewhat specialised monograph on the function theory of Cartan-Hadamard manifolds, which the authors conveniently define in the first sentence of the introduction as “complete simply-connected Riemannian manifolds of non-positive sectional curvature”. The “manifolds which possess a pole” is more precisely described in the second sentence by the property that the exponential mapping at each point is a diffeomorphism. (So these manifolds are homeomorphic to real or complex Euclidean spaces, which implies that they are non-compact and topologically trivial.)I was interested in this book particularly for the analysis of Jacobi fields, the Hessian operator, subharmonic functions, and some other aspects of function theory which could be relevant to existence/regularity theory for Dirichlet problems for elliptic or weakly elliptic second order operators (particularly the Laplacian) on convex sets in Riemannian manifolds. However, it turned out that this book was a little too specialised for my requirements. But clearly this book is of great value to those who do research on CH manifolds, Kähler manifolds and so forth. I have seen this book referred to many times in standard differential geometry textbooks. I think it would be excellent value for USD20.

⭐主なテーマはCartan-Hadamard 多様体（完備、単連結、リーマン多様体で非正の断面曲率をもつもの）で更にケーラーであれば（１）Ｃ＾ｎに双正則になる、（２）Ｃ＾ｎの有界領域に双正則になる、と予想されているある種の付加条件でケーラーを仮定しない場合の研究である。（１）は放物型、（２）は双曲型と考えられるから面白い研究であるが、ケーラーを仮定して予想を解けばどうなの？と言う気もするのであるが、ケーラーをはずしたらどこまでいえるか、というのも１つの研究法かもしれない 方法は当然微分幾何学的でそちらは勉強不足の私にはほとんど分からなかった。 ほとんど分からないって、そういう読書は意味ないんじゃないの、と思う人がいるかもしれないが、僕にとってはそうでもないですよ、ということである。

Keywords

Free Download Function Theory on Manifolds Which Possess a Pole (Lecture Notes in Mathematics, 699) 1979th Edition in PDF format
Function Theory on Manifolds Which Possess a Pole (Lecture Notes in Mathematics, 699) 1979th Edition PDF Free Download
Download Function Theory on Manifolds Which Possess a Pole (Lecture Notes in Mathematics, 699) 1979th Edition 1979 PDF Free
Function Theory on Manifolds Which Possess a Pole (Lecture Notes in Mathematics, 699) 1979th Edition 1979 PDF Free Download
Download Function Theory on Manifolds Which Possess a Pole (Lecture Notes in Mathematics, 699) 1979th Edition PDF
Free Download Ebook Function Theory on Manifolds Which Possess a Pole (Lecture Notes in Mathematics, 699) 1979th Edition