Differential Geometry and Complex Analysis

1. Front Matter

   Pages N1-XIII

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2. H. E. Rauch, Géomètre Différentiel

   • Par Marcel Berger

   Pages 1-13

3. H. E. Rauch, Function Theorist

   • Clifford J. Earle

   Pages 15-31

4. H. E. Rauch, Theta Function Practitioner

   • Hershel M. Farkas

   Pages 33-47

5. Some loci in Teichmüller Space for Genus Six Defined by Vanishing Thetanulls

   • Robert D. M. Accola

   Pages 49-63

6. Möbius Transformations and Clifford Numbers

   • Lars V. Ahlfors

   Pages 65-73

7. Polynomial Approximation in Quasidisks

   • J. M. Anderson, F. W. Gehring, A. Hinkkanen

   Pages 75-86

8. An Inequality for Riemann Surfaces

   • Lipman Bers

   Pages 87-93

9. Extremal Kähler Metrics II

   • Eugenio Calabi

   Pages 95-114

10. On the Characteristic Numbers of Complete Manifolds of Bounded Curvature and Finite Volume

    • Jeff Cheeger, Mikhael Gromov

    Pages 115-154

11. Deformation of Surfaces Preserving Principal Curvatures

    • Shiing-shen Chern

    Pages 155-163

12. One-Dimensional Metric Foliations in Constant Curvature Spaces

    • Detlef Gromoll, Karsten Grove

    Pages 165-168

13. The Existence of Three Short Closed Geodesics

    • Wilhelm Klingenberg

    Pages 169-179

14. On Lifting Kleinian Groups to SL (2, ℂ)

    • Irwin Kra

    Pages 181-193

15. On the Ends of Trajectories

    • Albert Marden, Kurt Strebel

    Pages 195-204

16. An Integrability Condition for Simple Lie Groups

    • Min-Oo, Ernst A. Ruh

    Pages 205-211

17. Uniqueness in the Cauchy Problem for a Degenerate Elliptic Second Order Equation

    • Louis Nirenberg

    Pages 213-218

18. On the Structure of Complete Manifolds with Positive Scalar Curvature

    • Shing Tung Yau

    Pages 219-222

19. Back Matter

    Pages 223-224

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This volume is dedicated to the memory of Harry Ernest Rauch, who died suddenly on June 18, 1979. In organizing the volume we solicited: (i) articles summarizing Rauch's own work in differential geometry, complex analysis and theta functions (ii) articles which would give the reader an idea of the depth and breadth of Rauch's researches, interests, and influence, in the fields he investigated, and (iii) articles of high scientific quality which would be of general interest. In each of the areas to which Rauch made significant contribution - pinching theorems, teichmiiller theory, and theta functions as they apply to Riemann surfaces - there has been substantial progress. Our hope is that the volume conveys the originality of Rauch's own work, the continuing vitality of the fields he influenced, and the enduring respect for, and tribute to, him and his accom­ plishments in the mathematical community. Finally, it is a pleasure to thank the Department of Mathematics, of the Grad­ uate School of the City University of New York, for their logistical support, James Rauch who helped us with the biography, and Springer-Verlag for all their efforts in producing this volume. Isaac Chavel . Hershel M. Farkas Contents Harry Ernest Rauch - Biographical Sketch. . . . . . . . VII Bibliography of the Publications of H. E. Rauch. . . . . . X Ph.D. Theses Written under the Supervision of H. E. Rauch. XIII H. E. Rauch, Geometre Differentiel (by M. Berger) . . . . . . . .

• Analysis
• Complex analysis
• Geometry
• Riemann surfaces
• calculus
• differential geometry

• The City College of the City University of New York, New York, USA

  Isaac Chavel

• Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

  Hershel M. Farkas

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