Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.2 9/5/84; site gloria.UUCP Path: utzoo!watmath!clyde!cbosgd!cbdkc1!desoto!packard!edsel!bentley!hoxna!houxm!whuxlm!harpo!decvax!genrad!mit-eddie!godot!harvard!seismo!rochester!rocksvax!rocksanne!sunybcs!gloria!colonel 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 References: <189@faron.UUCP> <18271@lanl.ARPA> Organization: SUNY-Buffalo Confuser Science Lines: 14 [_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