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Conference 1

Conference 1

COMMUNICATIONS IN MATHEMATICAL ANALYSIS, CONFERENCE 01, 2008

Proceedings of the Midwest Geometry Conference held at the University of Oklahoma at Norman, USA, May 5-7, 2006
The following papers were presented at conference, then refereed and accepted for publication in a special issue ofCommunications in Mathematical Analysis. For additional details on the conference, please contact Prof. En-Bing Lin (e-mail:enbing.lin@cmcih.edu)

PREFACE

In May of 2006, the Midwest Geometry Conference was held at The University of Oklahoma, Norman. For this conference, we invited specialists working in the areas of p-harmonic geometry, geometric flows, complex and Riemannian geometry, conformal geometry, convex geometry, minimal varieties, symmetric criticality, algebraic geometry, partial differential equations, geometric measure theory, and mathematical physics. In recent years, there have been enormous interactions in the above areas and we received a warm response to our invitations. Thirteen sixty-minute addresses and ten thirty-minute lectures were delivered, one sixty-minute "Panel discussions on open problems", and one forty-five minute "Future directions of the midwest geometry conference" were provided in the conference. Among them, there were six Ph.D. theses or theses-related works from the region of the Midwest presented, and the resolution of turning the Midwest Geometry Conference commencing 2008 from an annual event to a semi-annual one was reached. The full Conference Schedule was posted at the website HERE. The majority of papers in the present volume are expositions of these addresses and panel discussions.

In the final paper of this Proceedings, we include some open problems in geometry that are evolved from or generated in "Panel discussions on open problems" held after the Saturday night banquet of the Midwest Geometry Conference in the Commons Restaurant at The University of Oklahoma. The panel is comprised of the invited speakers and participants to whom we wish to express our gratitude. Special thanks to Professors Jianguo Cao, Robert M. Hardt, Wu-Yi Hsiang, Changyou Wang, Shihshu Walter Wei, and Henry C. Wente. We thank all colleagues who participated in the conference and contributed to this volume. The second editor is indebted to the National Science Foundation and the Department of Mathematics, the College of Arts and Sciences, and the Vice-President Office of Research of The University of Oklahoma for funding his proposals and for their generous support. We are also indebted to Communications in Mathematical Analysis for the publishing of this proceedings.

By Prof. En-Bing Lin (Department of Mathematics, Central Michigan University, Mt. Pleasant, MI 48859, USA) and Prof. Shihshu Walter Wei (Department of Mathematics, University of Oklahoma, Norman, OK 73019, USA)

CONTENTS

  1. I. G. Avramidi, Heat Kernel Asymptotics on Symmetric Spaces . Commun. Math. Anal. Conf. 1 (2008). pp. 1 - 10
  2. S. Lee, Weierstrass Representation for Timelike Minimal Surfaces in Minkowski 3-Space . Commun. Math. Anal. Conf. 1 (2008). pp. 11 - 19
  3. Z. Shen and C. Sormani, The Topology of Open Manifolds with Nonnegative Ricci Curvature . Commun. Math. Anal. Conf. 1 (2008). pp. 20 - 34
  4. J. F. Li and S. W. Wei, A p-Harmonic Approach to the Generalized Bernstein Problem . Commun. Math. Anal. Conf. 1 (2008). pp. 35 - 39
  5. S. W. Wei and L. Wu, Homotopy Groups and p-Harmonic Maps . Commun. Math. Anal. Conf. 1 (2008). pp. 40 - 45
  6. S. W. Wei, J. F. Li, and L. Wu, Generalizations of the Uniformization Theorem and Bochner's Method in p-Harmonic Geometry . Commun. Math. Anal. Conf. 1 (2008). pp. 46 - 68
  7. W. Y. Hsiang and E. Straume, An Equivariant Riemannian Geometric Approach to the 3-Body Problem in Celestial Mechanic . Commun. Math. Anal. Conf. 1 (2008). pp. 69 - 79
  8. E. B. Lin and S. W. Wei, Some Open Problems in Geometry . Commun. Math. Anal. Conf. 1 (2008). pp. 80 - 83