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From: gjk@talcott.UUCP (Greg J Kuperberg)
Newsgroups: net.math
Subject: Re: Re: Re: Strange Shapes
Message-ID: <159@talcott.UUCP>
Date: Mon, 3-Dec-84 13:12:36 EST
Article-I.D.: talcott.159
Posted: Mon Dec  3 13:12:36 1984
Date-Received: Thu, 6-Dec-84 06:12:52 EST
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Organization: Harvard
Lines: 17

> David Park asks:
>   Isn't the surface of maximal volume with a given finite surface areas always
> a sphere?
>   I expect so, but I'd like to see a proof. It's certainly true if the bounded
> region is a subset of a finite ball in 3-space (I mean the conjecture about
> finite area => finite volume), but I don't see any self-evident reason that
> it should be true for regions extending to infinity.

This is a difficult theorem, even in the case surfaces that are contained
in a finite-sized polyhedron.
---
			Greg Kuperberg
		     harvard!talcott!gjk

"Madam, there is only one important question facing us, and that is the
question whether the white race will survive."  -Leonid Breshnev, speaking
to Margaret Thatcher.