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1. Complex Analysis by Lars Ahlfors  
Hardcover: 336
Pages
(19790101)
 used & new: US$179.87 (price subject to change: see help) Asin: 0070006571 Average Customer Review: Canada  United Kingdom  Germany  France  Japan  
Editorial Review Product Description Customer Reviews (23)
Total Garbage
Excellent book
Complex analysis, Ahlfors
Tough
Classic book on complex analysis: one of the best, but overpriced 
2. Complex Analysis: An Introduction to the Theory of Analytic Fuctions of One Complex Variable by Lars V. Ahlfors  
Hardcover: 317
Pages
(1966)
Asin: B000FBLW5G Canada  United Kingdom  Germany  France  Japan  
3. Riemann Surfaces (Mathematics Series) by Lars V. Ahlfors, L. Sario  
Hardcover: 382
Pages
(196012)
Isbn: 0691080275 Canada  United Kingdom  Germany  France  Japan  
4. Complex Analysis  An Introduction to the Theory of Analytic Functions of One Complex Variable by Lars V Ahlfors  
Hardcover: 247
Pages
(1953)
Asin: B003B9FQW4 Canada  United Kingdom  Germany  France  Japan  
5. Lectures on Quasiconformal Mappings (University Lecture Series) by Lars V. Ahlfors  
Paperback: 162
Pages
(20060714)
list price: US$35.00  used & new: US$28.00 (price subject to change: see help) Asin: 0821836447 Average Customer Review: Canada  United Kingdom  Germany  France  Japan  
Editorial Review Product Description Customer Reviews (1)
Very clear and understandable exposition As the author notes, quasiconformal mappings were introduced by the mathematician H. Grotzsch in 1929 as mappings that are as close to conformal as possible, but that can, for example, take a square in the plane and map it to a (nonsquare) rectangle in the plane, mapping vertices onto vertices in the process. Conformal maps cannot do this, and a measure of how far the quasiconformal map is from being conformal involves the calculation of the dilatation at a point. The dilatation is computed by considering the effect that the linearization of a C1 homeomorphism has on circles. Such circles are mapped to ellipses, and the ratio of the major to the minor axis gives the dilatation. The dilatation is 1 for a conformal mapping. Following Grotzsch, a mapping is then said to be quasiconformal if the dilatation is bounded, and Kquasiconformal if the dilatation is less than or equal to K. For a family C of curves in the plane, the author introduces the extremal length of C, and shows that it is invariant under conformal mappings and "quasiinvariant" (multiplied by a bounded factor) under quasiconformal mappings. And following precedents from harmonic analysis, the author defines the Dirichlet integral, and shows it to be quasiinvariant under quasiconformal mappings. A more general definition of a quasiconformal mapping is then given, that relaxes the Grotzsch requirement that the mappings be C1. A (topological) mapping is called Kquasiconformal if the "modules" of quadrilaterals are Kquasiinvariant. Quadrilaterals are defined to be Jordan regions with a pair of disjoint arcs on the boundary. The "module" is then defined to be the ratio of the sides of the rectangle that the quadrilateral is mapped toconformally. A 1quasiconformal mapping is shown to be conformal under this new definition. This "geometric" definition of quasiconformal is followed by an "analytic" one, namely that a (topological) mapping is Kquasiconformal if it is "absolutely continuous on lines", with another condition that the ratio of its complex derivatives must be bounded by (K1)/(K+1). A function on a region is "absolutely continuous on lines" if it is absolutely continuous on almost every horizontal and vertical line of any rectangel in the region. The author proves that the geometric and analytic definitions are equivalent. The author then considers three different extremal problems for a doublyconnected region in a finite plane. The problem of finding the largest value of the module of this region is considered for three different conditions on this region and its bounded and unbounded components. Simple relations are shown to exist between the three different extremal modules. Also, and very interestingly, the author gives a connection between these extremal modules and elliptic curves. Mori's theorem is also proved, which gives a "Holder inequality", i.e. information on the "stretching" ability of Kquasiconformal mappings of the open unit disk to the open unit disk. This then allows a homeomorphic extension to the closed disk. The author then shows that Kquasiconformal mappings of the unit disk unto itself form a sequentially compact family with respect to uniform convergence. He then considers the question as to when quadruples of distinct complex numbers can be mapped to each other under Kquasiconformal mappings. These results naturally set up a study of the boundary value properties of quasiconformal mappings. The author proves an "Mcondition" that is satisfied by a boundary correspondence mapping. This condition involves the parameter K, and the author shows that the boundary values of a Kquasiconformal mapping must satisfy this condition. He then studies the extent to which quasiconformal mappings are isometries, called "quasiisometries" where distances are multiplied by a bounded factor. The author then gives an interesting discussion as to the geometric properties of curve that the real line gets mapped to when a quasiconformal mapping of the entire complex plane is considered. Attention is then concentrated on proving the existence of quasiconformal mappings with a given complex dilatation. This entails a solution of the Beltrami equation, and for this purpose the author constructs two different integral operators, one of which acts on Lp functions for p > 2, the other acting on C2 functions with compact support.All of his discussion has the flavor of classical harmonic analysis, with detailed attention given to the proof of the CalderonZygmund inequality. The author ends his book with a consideration of Teichmuller spaces, with attention given to the extent to which the classical theory of conformally equivalent Riemann surfaces can be generalized to the context of quasiconformal mappings. The Teichmuller space is thus defined as the collection of pairs of Riemann surfaces and sensepreserving quasiconformal mappings between them, with pairs being equivalent under homotopy. The familiar Beltrami and quadratic differentials make their appearance, and the image of the mapping of the unit ball of Beltrami differentials to the spece of quadratic differentials is shown to be open. The Teichmuller space is then shown to be an open subset of the space of quadratic differentials, with the Teichmuller metric giving the same metric as the norm in the space of quadratic differentials. This space has dimension 3g  3 when the starting Riemann surface has genus g, and with respect to the parameters of the basis of this space, one obtains a holomorphic family of Riemann surfaces. ... Read more 
6. Conformal Invariants: Topics in Geometric Function Theory (McGrawHill series in higher mathematics) by Lars V. Ahlfors  
Hardcover: 192
Pages
(197312)
 used & new: US$299.99 (price subject to change: see help) Asin: 0070006598 Average Customer Review: Canada  United Kingdom  Germany  France  Japan  
Customer Reviews (1)
great book about advanced topics in complex function theory 
7. Contributions to the Theory of Riemann Surfaces. (AM30) (Annals of Mathematics Studies)  
Paperback: 264
Pages
(19530801)
list price: US$55.00  used & new: US$12.99 (price subject to change: see help) Asin: 0691079390 Canada  United Kingdom  Germany  France  Japan  
8. Advances in the Theory of Riemann Surfaces. (AM66) (Annals of Mathematics Studies) by Lars Valerian Ahlfors, Lipman Bers  
Paperback: 430
Pages
(19710701)
list price: US$75.00  used & new: US$69.59 (price subject to change: see help) Asin: 069108081X Canada  United Kingdom  Germany  France  Japan  
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9. Finnish Mathematicians: Lars Ahlfors, Rolf Nevanlinna, Mikko Kaasalainen, Arto Salomaa, Jarl Waldemar Lindeberg, Ernst Leonard Lindelöf  
Paperback: 44
Pages
(20100915)
list price: US$14.14  used & new: US$14.13 (price subject to change: see help) Asin: 1157246753 Canada  United Kingdom  Germany  France  Japan  
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10. Conformal Invariants: Topics in Geometric Function Theory (Ams Chelsea Publishing) by Lars V. Ahlfors  
Hardcover: 160
Pages
(201012)
list price: US$35.00  used & new: US$35.00 (price subject to change: see help) Asin: 0821852701 Canada  United Kingdom  Germany  France  Japan  
11. Academics of the University of Helsinki: Lars Ahlfors, Rolf Nevanlinna, Artturi Ilmari Virtanen, Kaarlo Juho Ståhlberg, Teivo Teivainen  
Paperback: 192
Pages
(20100915)
list price: US$27.64  used & new: US$27.64 (price subject to change: see help) Asin: 1155313119 Canada  United Kingdom  Germany  France  Japan  
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12. LECTURES IN MEMORY OF LARS AHLFORS: ISRAEL MATHEMATICAL CONFERENCE PROCEEDINGS. by Robert & Mikhail Sodin (Editors). Brooks  
Paperback: 158
Pages
(2000)
Asin: B000MKPX7S Canada  United Kingdom  Germany  France  Japan  
13. Biography  Ahlfors, Lars V(alerian) (19071996): An article from: Contemporary Authors by Gale Reference Team  
Digital: 5
Pages
(20020101)
list price: US$9.95  used & new: US$9.95 (price subject to change: see help) Asin: B0007SHHL0 Canada  United Kingdom  Germany  France  Japan  
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14. SwedishSpeaking Finns: Linus Torvalds, Georg Henrik Von Wright, Jean Sibelius, Tove Jansson, Lars Ahlfors, Zachris Topelius  
Paperback: 628
Pages
(20100915)
list price: US$68.22  used & new: US$68.22 (price subject to change: see help) Asin: 1155907701 Canada  United Kingdom  Germany  France  Japan  
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15. Lars Valerian Ahlfors: Collected Papers, 19291955 (Contemporary Mathematicians) by Lars V. Ahlfors  
Hardcover: 544
Pages
(198212)
list price: US$285.00  used & new: US$227.90 (price subject to change: see help) Asin: 3764330759 Canada  United Kingdom  Germany  France  Japan  
16. American People of Finnish Descent: Pamela Anderson, Eero Saarinen, David Lynch, Lars Ahlfors, Gus Hall, Jaco Pastorius, Alfred Aho, Matt Damon  
Paperback: 540
Pages
(20100915)
list price: US$60.05  used & new: US$43.84 (price subject to change: see help) Asin: 1155779398 Canada  United Kingdom  Germany  France  Japan  
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17. Lars Valerian Ahlfors: An entry from Gale's <i>Science and Its Times</i> by Judson Knight  
Digital: 1
Pages
(2000)
list price: US$2.90  used & new: US$2.90 (price subject to change: see help) Asin: B0027UWW0C Canada  United Kingdom  Germany  France  Japan  
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18. Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complext Variable by Lars V. Ahlfors  
Hardcover:
Pages
(1953)
Asin: B001LY3OXO Canada  United Kingdom  Germany  France  Japan  
19. Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable, 3rd Edition by Lars Valerian Ahlfors  
Paperback:
Pages
(1979)
Asin: B000KZ65CW Canada  United Kingdom  Germany  France  Japan  
20. Complex Analysis: An Introduction to the Theory of Analytic Functions. Second Edition by Lars V. Ahlfors  
Hardcover: 317
Pages
(1966)
Asin: B000LY7XWS Canada  United Kingdom  Germany  France  Japan  
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