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Internet Message Format  |  1992-11-04  |  985 b 
  1. Path: sparky!uunet!ogicse!decwrl!sdd.hp.com!ux1.cso.uiuc.edu!news.cso.uiuc.edu!usenet
  2. From: sutin@helios.ucsc.edu (Brian Sutin)
  3. Newsgroups: sci.math.research
  4. Subject: Geometry Conjecture
  5. Message-ID: <1d9q1sINN9ms@darkstar.UCSC.EDU>
  6. Date: 5 Nov 92 00:31:56 GMT
  7. Article-I.D.: darkstar.1d9q1sINN9ms
  8. Sender: Daniel Grayson <dan@math.uiuc.edu>
  9. Organization: Lick Observatory UCSC
  10. Lines: 13
  11. Approved: Daniel Grayson <dan@math.uiuc.edu>
  12. Nntp-Posting-Host: helios.ucsc.edu
  13. X-Submissions-To: sci-math-research@uiuc.edu
  14. X-Administrivia-To: sci-math-research-request@uiuc.edu
  15.  
  16. I need the following result (which may be common knowledge):
  17.  
  18. Let D be a region of R^3 with a reasonable boundary S and let dS be any
  19. measure on the surface of D.  If
  20.  
  21.     INT(S){ 1/|x - y| dS(y) } = 1    for all x in D,
  22.  
  23. then D must be an R^3 ball.
  24.  
  25. Brian Sutin                sutin@lick.ucsc.edu
  26. Lick Observatory, UCSC            Santa Cruz, CA 95064
  27.     Fred:   "May I rescue you?"
  28.     Ginger: "No, thank you.  I prefer being in distress."
  29.