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The research of caloric morphism

Research Project

Project/Area Number 13640151
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionIBARAKI UNIVERSITY

Principal Investigator

SHIMOMURA Katsunori  IBARAKI Univ., college of Science, Associate Professor, 理学部, 助教授 (00201559)

Co-Investigator(Kenkyū-buntansha) NISHIO Masaharu  Osaka City Univ., Graduate School of Science, Associate professor, 大学院・理学研究科, 助教授 (90228156)
SUZUKI Noriaki  Nagoya Univ., Graduate School of Mathematics, Associate professor, 大学院・多元数理科学研究科, 助教授 (50154563)
HORIUCHI Toshio  IBARAKI Univ., college of Science, Professor, 理学部, 教授 (80157057)
ANDO Hiroshi  IBARAKI Univ. college of Science, Research Associate, 理学部, 助手 (60292471)
Project Period (FY) 2001 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,600,000)
Fiscal Year 2002: ¥1,100,000 (Direct Cost: ¥1,100,000)
Fiscal Year 2001: ¥1,500,000 (Direct Cost: ¥1,500,000)
Keywordscaloric morphism / Appell transformation / heat equation / 熱方程式 / 多重熱作用素の解
Research Abstract

On caloric morphisms between manifolds, we obtained the following results :
1. The characterization theorem for caloric morphism between semi-riemannian manifolds, as a generalization of the reimannian case.
2. The time variable change and the space dilatation may depend on the space variable for caloric morphisms between semi-riemannian manifolds.
3. The time direction need not be preserved for caloric morphisms between semi-riemannian manifolds.
4. Above 2, 3, and 4 imply that the properties "independence of the time variable change and the space dilatation from the space variable" and "preservation of the time direction" of caloric morphism are the results of the ellipticity of the Laplacian.
5. The equation which characterize the caloric morphism is the same as the heat equation with respect to the weighted tension field.
6. Extension of the Appell transformations to the case of semi-euclidean spaces.
7. The determination of the caloric morphism between semi-euclidean spaces of same dimensions.
8. The determination of the caloric morphism on punctured euclidean space of radial riemannian metric.
9. The determination of the caloric morphism which translates the origin on punctured euclidean space of radial riemannian metric in the case that the dimension is greater than 2.
10. The determination of the caloric morphism on punctured euclidean space of radial semi-riemannian metric.
On the transformation preserving poly-temperatures, we obtained the following results :
The characterization theorem for the transformation preserving poly-temperatures, as a generalization of the caloric merphism. The relation between the transformation preserving poly-temperatures and caloric morphisms.

Report

(3 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • Research Products

    (32 results)

All Other

All Publications (32 results)

  • [Publications] Masaharu Nishio, Katsunori Shimomura: "A characterization of caloric morphisms between manifolds"Ann. Acad. Sci. Fenn. Math.. 28. 111-122 (2003)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Katsunori Shimomura: "Caloric morphisms on R^n\setminus{0} with respect to radial metrics"京都大学数理解析研究所講究録. 1293. 168-174 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Katsunori Shimomura: "On transformations which preserve poly-temperatures of degree $m$"Math. J, Ibaraki Univ.. 33. 23-34 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Toshio Horiuchi: "Removable singularities for quasilinear degenerate elliptic equations with absorption term"J. Math. Soc. Japan. 53(3). 513-540 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Toshio Horiuchi: "Some remarks on Kato's inequality"J. Inequal. Appl.. 6(1). 29-36 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Noriaki Suzuki: "Mean value property for temperatures on an annulus domain"京都大学数理解析研究所講究録. 1293. 168-174 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Noriaki Suzuki, Niel A.Watson: "A characterization of heat ball by mean value property for temperatures"Proc. Amer. Math. Soc.. 129. 2709-2713 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Teruo Ikegami, Masaharu Nishio: "$Q$-compactification of harmonic spaces and the Choquet simplex"Osaka J. Math.. 39(4). 931-944 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Hiroshi Ando, Yoshinori Morimoto: "Wick calculus and the Cauchy problem for some dispersive equations"Osaka J. Math.. 39(1). 123-147 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Katsunori Shimomura: "On transformations which preserve poly-temperatures of degree $m$"Math. J. Ibaraki Univ.. 33. 23-34 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Masaharu Nishio and Katsunori Shimomura: "A characterization of caloric morphisms between manifolds"Ann. Acad. Sci. Fenn. Math.. 28. 111-122 (2003)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Katsunori Shimomura: "Caloric morphisms on $\mathbb R^^n \setminus\{0\}$ with respect to radial metrics"Surikaisekikeukyusho Kokyurokuu. 1293. 150-153 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Masaharu Nishio and Katsunori Shimomura: "Caloric morphisms on semi-Euclidean space"Proceedings of International Conference on Complex Analysis and Related Topics, "The IX th Romanian-Finnish Seminar", Brasov.. to appear.

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Toshio Horiuchi: "Removable singularities for quasilinear degenerate elliptic equations with absorption term"J. Math. Soc. Japan. 53. 513-540 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Toshio, Horiuchi: "Some remarks on Kato's inequality"J. Inequal. Appl.. 6. 29-36 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Noriaki. Suzuki and Neil A. Watson: "A characterization of heat balls by a mean value property for temperatures"Proc. Amer. Math. Soc.. 129. 2709-2713 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Noriaki. Suzuki: "Mean value property for temperatures on an annulus domain"Surikaisekikenkyusho Kokyuroku. 1293. 168-174 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Teruo Ikegami and Masaharu Nishio: "$Q$-compactification of harmonic spaces and the Choquet simplex"Osaka. J. Math.. 39. 931-944 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Hiroshi Ando and Yoshinori Morimoto: "Wick calculus and the Cauchy problem for some dispersive equations"Osaka. J. Math.. 39. 931-944 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Masaharu Nishio, Katsunori Shimomura: "A characterization of caloric morphisms between manifolds"Ann. Acad. Sci. Fenn. Math.. 28. 111-122 (2003)

    • Related Report
      2002 Annual Research Report
  • [Publications] Katsunori Shimomura: "Caloric morphisms on R^n\setminus{0} with respect to radial metrics"京都大学数理解析研究所講究録. 1293. 168-174 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Katsunori Shimomura: "On transformations which preserve poly-temperatures of degree $m$"Math. J. Ibaraki Univ.. 33. 23-34 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] Toshio Horiuchi: "Removable singularities for quasilinear degenerate elliptic equations with absorption term"J. Math. Soc. Japan. 53(3). 513-540 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] Toshio Horiuchi: "Some remarks on Kato's inequality"J. Inequal. Appl.. 6(1). 29-36 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] Noriaki Suzuki: "Mean value property for temperatures on an annulus domain"京都大学数理解析研究所講究録. 1293. 168-174 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Noriaki Suzuki, Niel A.Watson: "A characterization of heat ball by mean value property for temperatures"Proc. Amer. Math. Soc.. 129. 2709-2713 (2001)

    • Related Report
      2002 Annual Research Report
  • [Publications] Teruo Ikegami, Masaharu Nishio: "$Q$-compactification of harmonic spaces and the Choquet simplex"Osaka J. Math.. 39(4). 931-944 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Hiroshi Ando, Yoshinori Morimoto: "Wick calculus and the Cauchy problem for some dispersive equations"Osaka J. Math.. 39(1). 123-147 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Katsunori Shimomura: "On transformations which preserve poly-temperatures of degree m"Mathematical Journal of Ibaraki University. 33. 23-34 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Toshio Horiuchi: "Removable singularities for quasilinear degenerate elliptic equations with absorption term"J. Math. Soc. Japan. 53・3. 513-540 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Noriaki Suzuki, Niel A. Watson: "A characterization of heat balls by mean value property for temperatures"Proc. Amer. Math. Soc.. 129. 2709-2713 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Teruo Ikegami, Masaharu Nishio: "Q-compactification of harmonic spaces and the choquet simplex"Osaka J. of Math.. (発表予定).

    • Related Report
      2001 Annual Research Report

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Published: 2001-04-01   Modified: 2016-04-21  

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