The Jacobian, the square root and the set ∞ |
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Authors: | Fabrice Bethuel |
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Institution: | UPMC Université Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions, F-75005 Paris, France |
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Abstract: | In these notes, we wish to present a new approach to the problem of prescribing Jacobian determinants in dimension two: we restrict ourselves to the case the datum is a finite sum of Dirac masses. The main point is to show that we may relate this problem to the search of harmonic maps into a singular space shaped as the symbol ∞. The later problem in turn is closely linked to questions in complex analysis. A large part of the paper is devoted to a presentation of these mathematical objects and their connections. |
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Keywords: | Singular harmonic map Jacobian determinant Dirac mass Renormalized energy |
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