@article{84e6b68022704b69b0121629bbbce14b,
title = "A Remark on Finite Type Conditions",
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.",
keywords = "Faa di Bruno formula, Finite type conditions, Plurisubharmonic function, Positivity property, Real hypersurface germ",
author = "D{\textquoteright}Angelo, {John P.}",
note = "Funding Information: Acknowledgements The author thanks the referee for suggesting some clarifications. The author particularly thanks Jeff McNeal for noting the author{\textquoteright}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.",
year = "2018",
month = jul,
day = "1",
doi = "10.1007/s12220-017-9921-1",
language = "English (US)",
volume = "28",
pages = "2602--2608",
journal = "Journal of Geometric Analysis",
issn = "1050-6926",
publisher = "Springer New York",
number = "3",
}