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Open AccessArticle

Volume Preserving Maps Between p-Balls

Department of Mathematics, Technical University of Cluj-Napoca, str. Memorandumului 28, RO-400114 Cluj-Napoca, Romania
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Symmetry 2019, 11(11), 1404; https://doi.org/10.3390/sym11111404
Received: 19 October 2019 / Revised: 8 November 2019 / Accepted: 12 November 2019 / Published: 14 November 2019
(This article belongs to the Special Issue Symmetry in Applied Mathematics)
We construct a volume preserving map U p from the p-ball B p ( r ) = x R 3 , x p r to the regular octahedron B 1 ( r ) , for arbitrary p > 0 . Then we calculate the inverse U p 1 and we also deduce explicit expressions for U and U 1 . This allows us to construct volume preserving maps between arbitrary balls B p ( r ) and B p ( r ˜ ) , and also to map uniform and refinable grids between them. Finally we list some possible applications of our maps. View Full-Text
Keywords: equal volume projection; hierarchical grid equal volume projection; hierarchical grid
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Holhoş, A.; Roşca, D. Volume Preserving Maps Between p-Balls. Symmetry 2019, 11, 1404.

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