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A Remark on Finite Type Conditions

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Abstract

We prove that a certain positivity condition, considerably more general than pseudoconvexity, enables one to conclude that the regular and singular orders of contact agree when either of these numbers is 4.

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Acknowledgements

The author thanks the referee for suggesting some clarifications. The author particularly thanks Jeff McNeal for noting the author’s omission in [5] and for sharing versions of the preprint [12] with him. The author acknowledges useful discussions with Dmitri Zaitsev, Siqi Fu, and Ming Xiao. The important preprint [13] by Zaitsev makes a systematic study of fourth-order invariants, but it does not include our Theorem 1.1. The author acknowledges support from NSF Grant DMS 13-61001.

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  1. Department of Mathematics, University of Illinois, 1409 W. Green St., Urbana, IL, 61801, USA

    John P. D’Angelo

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  1. John P. D’Angelo
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Correspondence to John P. D’Angelo.

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D’Angelo, J.P. A Remark on Finite Type Conditions. J Geom Anal 28, 2602–2608 (2018). https://doi.org/10.1007/s12220-017-9921-1

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  • DOI: https://doi.org/10.1007/s12220-017-9921-1

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