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Higher Dimensional Conundra

Steven G. Krantz


In recent years, especially in the subject of harmonic analysis, there has been interest in geometric phenomena of RN as N → ∞. In the present paper we examine several specific geometric phenomena in Euclidean space and calculate the asymptotics as the dimension gets large.

Author Information

Steven G. Krantz received his B.A. degree from the University of California at Santa Cruz in 1971. He earned the Ph.D. from Princeton University in 1974. He has taught at UCLA, Princeton University, Penn State, and Washington University in St. Louis. Krantz is the holder of the UCLA Alumni Foundation Distinguished Teaching Award, the Chauvenet Prize, and the Beckenbach Book Prize. He is the author of 150 papers and 50 books. His research interests include complex analysis, real analysis, harmonic analysis, and partial differential equations. Krantz is currently the Deputy Director of the American Institute of Mathematics.

American Institute of Mathematics, 360 Portage Avenue,
Palo Alto, CA 94306

Technologies Used in This Article


  • geometry
  • Euclidean space
  • volume
  • dimension
  • centroid

Publication data

  • Published Ocober, 2007; article ID 1612
  • Copyright © 2007, by Steven G. Krantz

Article Link

Steven G. Krantz, "Higher Dimensional Conundra," Convergence (October 2007)


Journal of Online Mathematics and its Applications