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From: colonel@gloria.UUCP (George Sicherman)
Newsgroups: net.math
Subject: Re: strange shapes
Message-ID: <734@gloria.UUCP>
Date: Thu, 20-Dec-84 12:11:35 EST
Article-I.D.: gloria.734
Posted: Thu Dec 20 12:11:35 1984
Date-Received: Sun, 23-Dec-84 00:36:34 EST
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Organization: SUNY-Buffalo Confuser Science
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[_Black Hole_]

> Actually, I don't think there is a finite surface that 'encloses' infinite
> volume.  And I think that a sphere probably does enclose the maximal
> volume for a given area.  But there have been no proofs yet.

A finite surface that encloses an infinite volume?  How about a Klein Bottle?

If you insist on an orientable surface, see Kellogg on Potential Theory.  His
proof of Gauss's theorem will give you some ideas about what restrictions
are necessary.
-- 
Col. G. L. Sicherman
...seismo!rochester!rocksanne!rocksvax!sunybcs!gloria!colonel