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Uniform geometric estimates of sublevel sets

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Abstract

This paper reconsiders the uniform sublevel set estimates of Carbery, Christ, and Wright [7], Phong, Stein, and Sturm [23], and Carbery and Wright [8] from a geometric perspective. This perspective leads one to consider a natural collection of homogeneous, nonlinear differential operators, which generalize mixed derivatives in ℝ d . As a consequence, it is shown that, in comparison to these previous works, improved uniform estimates are possible in all but certain explicitly “flat” situations.

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Authors and Affiliations

  1. Department of Mathematics, University of Pennsylvania, Philadelphia, PA, 99104, USA

    Philip T. Gressman

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  1. Philip T. Gressman
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Correspondence to Philip T. Gressman.

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This research was partially supported by NSF grant DMS-0850791.

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Gressman, P.T. Uniform geometric estimates of sublevel sets. JAMA 115, 251–272 (2011). https://doi.org/10.1007/s11854-011-0029-4

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  • DOI: https://doi.org/10.1007/s11854-011-0029-4

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