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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A note on pseudoconvex hypersurfaces of infinite type in $\mathbb C^n$
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by John Erik Fornæss and Ninh Van Thu PDF
Proc. Amer. Math. Soc. 148 (2020), 4435-4444 Request permission


The purpose of this article is to prove that there exists a real smooth pseudoconvex hypersurface germ $(M,p)$ of D’Angelo infinite type in $\mathbb {C}^{n+1}$ such that it does not admit any (singular) holomorphic curve in $\mathbb {C}^{n+1}$ tangent to $M$ at $p$ to infinite order.
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Additional Information
  • John Erik Fornæss
  • Affiliation: Department of Mathematics, NTNU, Sentralbygg 2, Alfred Getz vei 1, 7491 Trondheim, Norway
  • MR Author ID: 68145
  • Email:
  • Ninh Van Thu
  • Affiliation: Department of Mathematics, VNU University of Science, Vietnam National University at Hanoi, 334 Nguyen Trai, Thanh Xuan, Hanoi, Vietnam; Thang Long Institute of Mathematics and Applied Sciences, Nghiem Xuan Yem, Hoang Mai, Hanoi, Vietnam
  • MR Author ID: 853151
  • Email:
  • Received by editor(s): October 28, 2019
  • Received by editor(s) in revised form: March 5, 2020
  • Published electronically: July 20, 2020
  • Additional Notes: The second author was supported by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 101.02-2017.311.
  • Communicated by: Harold Boas
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 148 (2020), 4435-4444
  • MSC (2010): Primary 32T25; Secondary 32C25
  • DOI:
  • MathSciNet review: 4135308