Topics on Real and Complex Singularities PDF
Preview Topics on Real and Complex Singularities
TOPICS REAL ON AND COMPLEX SINGULARITIES 9115_9789814596039_tp.indd 1 27/1/14 11:45 am May2,2013 14:6 BC:8831-ProbabilityandStatisticalTheory PST˙ws TThhiiss ppaaggee iinntteennttiioonnaallllyy lleefftt bbllaannkk TOPICS REAL ON AND COMPLEX SINGULARITIES Proceedings of the 4th Japanese–Australian Workshop (JARCS4) Kobe, Japan 22 – 25 November 2011 Editors Satoshi Koike Hyogo University of Teacher Education, Japan Toshizumi Fukui Saitama University, Japan Laurentiu Paunescu University of Sydney, Australia Adam Harris University of New England, Australia Alexander Isaev Australian National University, Australia World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TAIPEI • CHENNAI 9115_9789814596039_tp.indd 2 27/1/14 11:45 am Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. TOPICS ON REAL AND COMPLEX SINGULARITIES Proceedings of the 4th Japanese–Australian Workshop (JARCS4) Copyright © 2014 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 978-981-4596-03-9 Printed in Singapore gk.indd 1 27/1/2014 9:05:24 AM January 17, 2014 17:13 BC:9115-JARCS4Proceeding Topics v Preface The fourth Japanese-Australian Workshop on Real and Complex Sin- gularities (JARCS4 KOBE 2011) was held at the Kobe Satellite of Hyogo University of Teacher Education during the period 22-25 November, 2011. There were 31 participants from Australia and Japan. The Australian and Japanese Singularity Theory specialists have built up a strong research relationship in the past three decades. For instance, the blow-analytic theory introduced by Tzee-Char Kuo in Australia has been intensively developed in Japan. In addition, a lot of joint works by researchersofbothcountrieshavebeenestablishedinseveraltopicsrelated to real and complex singularities. The present volume consists mainly of the texts of the invited talks of the workshop. Some of them are joint works of Australians and Japanese. Thisvolumecontainsoriginalarticlesonrealandcomplexsingularities, topology of differentiable maps, openings of differentiable map-germs, the relationshipbetween free divisors and holonomic systems, effective compu- tational method of invariantsof singularities,the applicationofsingularity theory to differential geometry, the deformation theory of CR structures and differential equations with singular points. In these articles some im- portant new notions for characterizations of singularities are introduced, and several new results are presented. New approaches to classical topics and new computational methods of singularities are also presented. We would like to thank the contributors for their cooperation. All the articlesinthisvolumehavebeenverycarefullyrefereed.Wewouldalsolike to thank the referees for taking time to read and give a lot of comments again and again. The workshop was supported by the Grant-in-Aid for Scientific Re- searches No. 23244008(Investigator: Osamu Saeki), No. 22340030(Investigator: Goo Ishikawa), No. 23540099(Investigator: Kimio Miyajima), No. 21540054(Investigator: Shuzo Izumi), No. 23540087(Investigator: Satoshi Koike) January 17, 2014 17:13 BC:9115-JARCS4Proceeding Topics vi of the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan, and Hyogo University of Teacher Education. We ac- knowledge the support. 18 September 2013 Satoshi Koike January 17, 2014 17:13 BC:9115-JARCS4Proceeding Topics vii Organizing Committees of the fourth Japanese-AustralianWorkshop on Real and Complex Singularities Satoshi Koike (Chairman) – Hyogo University of Teacher Education, Japan Toshizumi Fukui – Saitama University, Japan Laurentiu Paunescu – University of Sydney, Australia Adam Harris – University of New England, Australia Alexander Isaev – Australian National University, Australia January 17, 2014 17:13 BC:9115-JARCS4Proceeding Topics viii List of Participants Takao Akahori (Hyogo University, Japan) Kana Ando (Chiba University, Japan) Takuo Fukuda (Nihon University, Japan) Toshizumi Fukui (Saitama University, Japan) Hirofumi Hagi (Hyogo University of Teacher Education, Japan) Adam Harris (University of New England, Australia) Jonathan Hillman (University of Sydney, Australia) Goo Ishikawa (Hokkaido University, Japan) Shuzo Izumi (Kinki University, Japan) Shigeyasu Kamiya (Okayama University of Science, Japan) Yoshihiro Kawazoe (Hyogo University of Teacher Education, Japan) Yumiko Kitagawa (Oita National College of Technology, Japan) Naoki Kitazawa (Tokyo Institute of Technology, Japan) Mahito Kobayashi (Akita University, Japan) Satoshi Koike (Hyogo University of Teacher Education, Japan) Yutaka Matsui (Kinki University, Japan) Kimio Miyajima (Kagoshima University, Japan) Masayuki Nishioka (Kyushu University, Japan) Masao Ogawa (Hyogo University of Teacher Education, Japan) Mutsuo Oka (Tokyo University of Science, Japan) Tomohiro Okuma (Yamagata University, Japan) Laurentiu Paunescu (University of Sydney, Australia) Osamu Saeki (Kyushu University, Japan) JiroSekiguchi(TokyoUniversityofAgricultureandTechnology,Japan) Ryuhei Shigematsu (Hyogo University of Teacher Education, Japan) Masahiro Shiota (Nagoya University, Japan) Shinichi Tajima (Tsukuba University, Japan) Kiyoshi Takeuchi (Tsukuba University, Japan) Takahiro Yamamoto (Kyushu Sangyo University, Japan) Wataru Yukuno (Hokkaido University, Japan) Ruibin Zhang (University of Sydney, Australia) January 23, 2014 9:14 BC:9115-JARCS4Proceeding Topics ix Contents Preface v Organizing Committees vii List of Participants viii On the CR Hamiltonian flows and CR Yamabe problem 1 T. Akahori An example of the reduction of a single ordinary differential equation to a system, and the restricted Fuchsian relation 13 K. Ando Fronts of weighted cones 31 T. Fukui and M. Hasegawa Involutive deformations of the regular part of a normal surface 51 A. Harris and K. Miyajima Connected components of regular fibers of differentiable maps 61 J. T. Hiratuka and O. Saeki The reconstruction and recognition problems for homogeneous hypersurface singularities 75 A. V. Isaev Openings of differentiable map-germs and unfoldings 87 G. Ishikawa Non concentration of curvature near singular points of two variable analytic functions 115 S. Koike, T.-C. Kuo and L. Paunescu
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