Geometric properties of the sections of solutions to the Monge-Ampère equation
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- by Cristian E. Gutiérrez and Qingbo Huang PDF
- Trans. Amer. Math. Soc. 352 (2000), 4381-4396 Request permission
Abstract:
In this paper we establish several geometric properties of the cross sections of generalized solutions $\phi$ to the Monge-Ampère equation $\det D^{2}\phi = \mu$, when the measure $\mu$ satisfies a doubling property. A main result is a characterization of the doubling measures $\mu$ in terms of a geometric property of the cross sections of $\phi$. This is used to obtain estimates of the shape and invariance properties of the cross sections that are valid under appropriate normalizations.References
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Additional Information
- Cristian E. Gutiérrez
- Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
- Email: gutier@math.temple.edu
- Qingbo Huang
- Affiliation: Department of Mathematics, Temple University, Philadelphia, Pennsylvania 19122
- Address at time of publication: Department of Mathematics, University of Texas at Austin, Austin, Texas 78712
- Email: qhuang@math.utexas.edu
- Received by editor(s): June 9, 1997
- Published electronically: May 12, 2000
- Additional Notes: The first author was partially supported by NSF grant DMS-9706497
- © Copyright 2000 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 352 (2000), 4381-4396
- MSC (1991): Primary 35J60, 35D10; Secondary 26B25
- DOI: https://doi.org/10.1090/S0002-9947-00-02491-0
- MathSciNet review: 1665332