Discrete Isothermic Surfaces in Lie Sphere Geometry
暫譯: 李氏球幾何中的離散等溫面

本書提供了一種高度可接近的離散曲面理論方法，從整合系統中根植於曲面的變換理論的角度，置於莫比烏斯（Moebius）和李球幾何（Lie sphere geometry）的統一框架內。它闡明了平滑曲面的變換理論如何作為理解某些類型曲面離散化過程的跳板，並且針對高年級本科生、研究生及專業數學家。讀者將從對曲面變換理論的詳細探討中受益，包括特定類別曲面的克里斯托費爾（Christoffel）、卡拉普索（Calapso）和達布克斯（Darboux）變換，並且在平滑和離散環境中，通過零曲率表示法，包括平坦連接和守恆量，對整合系統有更深入的了解。

Joseph Cho is a differential geometer with a primary interest in the integrable systems approach to smooth and discrete surface theory. His studies in mathematics led to a bachelor's degree from the University of California, Berkeley, a master's degree from Korea University, and a doctorate from Kobe University. He has also worked as a postdoctoral researcher at TU Wien and is currently enjoying life as an assistant professor at Handong Global University, Republic of Korea.

Kosuke Naokawa is an associate professor at Hiroshima Institute of Technology in Japan. He received his PhD from Tokyo Institute of Technology in 2013, and subsequently conducted postdoctoral research in Kobe and Vienna. His research focuses on the geometry and topology of surfaces with singularities and their discretizations.

Yuta Ogata is a researcher in the field of surface theory, integrable systems, and singularity theory. He obtained his PhD from Kobe University in 2017. After working in Okinawa, Japan, he is currently an associate professor at Kyoto Sangyo University, Japan.

Mason Pember is a lecturer of mathematics at the University of Bath, United Kingdom. He obtained his PhD from the University of Bath in 2015 and subsequently held postdocs in Kobe, Vienna and Turin. His research is in differential geometry, specialising in topics such as integrable systems, surface theory and Lie sphere geometry.

Wayne Rossman is a professor of mathematics at Kobe University, Japan. He earned his PhD from the University of Massachusetts, Amherst in 1992, and has been working ever since in the Japanese differential geometry community, interspersed with post-doctoral positions and sabbaticals in California, Brazil, Bath England, Berlin and Vienna. His expertise lies in the differential geometry of surfaces and its discretization.

Masashi Yasumoto is an associate professor at Tokushima University, Japan. He obtained his PhD from Kobe University in 2015, and subsequently conducted his research at Tübingen, Osaka, and Fukuoka as a postdoctoral researcher. His research focuses on differential and discrete differential geometry of surfaces.

Joseph Cho 是一位微分幾何學家，主要關注於可積系統在平滑和離散曲面理論中的應用。他在數學方面的研究使他獲得了加州大學伯克利分校的學士學位、韓國大學的碩士學位，以及神戶大學的博士學位。他曾在維也納科技大學擔任博士後研究員，目前在韓國的韓東全球大學擔任助理教授，享受著他的生活。 Kosuke Naokawa 是日本廣島工業大學的副教授。他於2013年在東京工業大學獲得博士學位，隨後在神戶和維也納進行博士後研究。他的研究專注於具有奇異點的曲面的幾何和拓撲及其離散化。 Yuta Ogata 是一位專注於曲面理論、可積系統和奇異性理論的研究員。他於2017年在神戶大學獲得博士學位。在日本沖繩工作後，他目前是日本京都產業大學的副教授。 Mason Pember 是英國巴斯大學的數學講師。他於2015年在巴斯大學獲得博士學位，隨後在神戶、維也納和都靈擔任博士後研究員。他的研究領域是微分幾何，專注於可積系統、曲面理論和李球幾何等主題。 Wayne Rossman 是日本神戶大學的數學教授。他於1992年在美國馬薩諸塞州大學阿默斯特分校獲得博士學位，從此一直在日本的微分幾何社群中工作，期間曾在加州、巴西、英國巴斯、柏林和維也納擔任博士後職位和休假。他的專長在於曲面的微分幾何及其離散化。 Masashi Yasumoto 是日本德島大學的副教授。他於2015年在神戶大學獲得博士學位，隨後作為博士後研究員在圖賓根、大阪和福岡進行研究。他的研究專注於曲面的微分和離散微分幾何。