Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/3/84; site talcott.UUCP Path: utzoo!watmath!clyde!bonnie!akgua!whuxlm!harpo!decvax!genrad!wjh12!talcott!gjk 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 References: ubu.341, <176@ihnet.UUCP>, <177@ihnet.UUCP> <7116@watrose.UUCP> <136@talcott.UUC <1651@browngr.UUCP> 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.