Existence of hypersurfaces of prescribed mean curvature /
Suppose W is a smooth domain in Rn+1 with Ln+l(W) < ², H :
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| Format: | Thesis Book |
| Language: | English |
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[Place of publication not identified] :
[publisher not identified] ;
1994.
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| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=741965311&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | Suppose W is a smooth domain in Rn+1 with Ln+l(W) < ², H : W--- R is a continuous function with fW (h)n+1 dLn+1 <² and (H(x)) < HaW(x) for all x E W, where 'HW is the mean curvature for W. If B is a nonzero (n- l)-dimensional integral boundary such that spt(B) is a smooth, compact (n - l)-dimensional submanifold of W, then there exists an n- dimensional integral current T with spt(T) c Q and OT = B such that T has prescribed mean curvature H and spt(T) - spt(B) is a smooth, n-dimensional submanifold of Q except perhaps for a compact singular set of Hausdorff dimension at most (n - 7). If B is a closed set of Q and if there exists an appropriate triple cover of W , B, then there exists an n-dimensional flat chain modulo 3 R with Spt3 (R) c W - B and Spt3 (aR) c B such that R has prescribed mean curvature H for IIRI 13 -almost all points x E Spt3 (R). |
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| Item Description: | Vita. "Major Subject: Mathematics". |
| Physical Description: | vi, 64 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilms Inc. |
| Bibliography: | Includes bibliographical references. |