Modern History of Parabolic Equations on a Riemannian manifold

리이만 다양체에서 포물형 편미분 방정식에 관한 근현대사 고찰

  • 장정욱 (단국대학교 수학교육과)
  • Received : 2011.01.05
  • Accepted : 2011.02.19
  • Published : 2011.02.28

Abstract

Partial differential equations on a Riemannain manifold is one of the most important areas in differential geometry. In this article, we survey the role of parabolic equations on some of the main results of differential geometry and topology, especially in the modern mathematical history. Also, we introduce some recent research in this area.

라이만 다양체 위에서의 편미분 방정식의 연구는 미분기하학에서 중요한 연구 분야로 인식되어 왔다. 본 논문에서는 특히 최근에 미분기하학과 위상수학 분야에서 중요한 역할을 하고 있는 리이만 다양체 위에서의 포물형 방정식에 관한 역사적으로 주목받고 있는 중요한 연구 결과를 정리해 보고, 아울러 이 분야의 최근 연구 결과를 고찰한다.

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