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Minimal graphs in R3 over convex domains

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Permanent URL	http://hdl.lib.byu.edu/1877/1321
Title	Minimal graphs in R3 over convex domains
BYU Creator	Dorff, Michael
Keywords	convex domain; minimal graph; conjugate surfaces; associate surfaces; harmonic univalent mappings
Description/Abstract	Krust established that all conjugate and associate surfaces of a minimal graph over a convex domain are also graphs. Using a convolution theorem from the theory of harmonic univalent mappings, we generalize Krust's theorem to include the family of convolution surfaces which are generated by taking the Hadamard product or convolution of mappings. Since this convolution involves convex univalent analytic mappings, this family of convolution surfaces is much larger than just the family of associated surfaces. Also, this generalization guarantees that all the resulting surfaces are over close-toconvex domains. In particular, all the associate surfaces and certain Goursat transformation surfaces of a minimal graph over a convex domain are over close-to-convex domains.
Source	Proceedings of the American Mathematical Society, Vol 132, no 2, pp. 491-498.;
Publisher	First published in Proceedings of the American Mathematical Society Vol 132, no 2, published by the American Mathematical Society.
Date Original	2003-06-18
Language	English eng en
Publication Type	Articles
Type	Text
Format	application/pdf
Owning Institution	Brigham Young University
BYU College	College of Physical and Mathematical Sciences
BYU Department	Mathematics
Copyright Status	(c) 2003 The American Mathematical Society.;
Copyright Use Information	http://www.lib.byu.edu/generic_copyright.html

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