Collected Works

While Eugenio Calabi is best known for his contributions to the theory of Calabi-Yau manifolds, this Steele-Prize-winning geometer’s fundamental contributions to mathematics have been far broader and more diverse than might be guessed from this one aspect of his work. His works have deep influence and lasting impact in global differential geometry, mathematical physics and beyond. By bringing together 47 of Calabi’s important articles in a single volume, this book provides a comprehensive overview of his mathematical oeuvre, and includes papers on complex manifolds, algebraic geometry, Kähler metrics, affine geometry, partial differential equations, several complex variables, group actions and topology. The volume also includes essays on Calabi’s mathematics by several of his mathematical admirers, including S.K. Donaldson, B. Lawson and S.-T. Yau, Marcel Berger; and Jean Pierre Bourguignon. This book is intended for mathematicians and graduate students around the world. Calabi’s visionary contributions will certainly continue to shape the course of this subject far into the future.

• 53C55, 32F07, 35J96, 53A10, 53A15, 53C21, 53C24, 53C26
• Calabi Yau manifold
• Calabi Conjecture
• Kaehler Einstein metrics
• extremal Kaehler metrics and harmonic map from S^2 to S^n
• Collected Works
• Eugenio Calabi

“In my case, I spent several happy hours learning about affine differential geometry, something that would certainly never have happened if I had not picked up this volume. … The collected works of Eugenio Calabi are worthy of a place on the bookshelf of any person with a serious interest in differential geometry.” (Joel Fine, EMS Magazine, May 11, 2023)

• Le Bois-Marie, Inst Hautes Etudes Scientifiques, BURES SUR YVETTE, France

  Jean-Pierre Bourguignon

• Mathematics Department, Stony Brook University, Stony Brook, USA

  Xiuxiong Chen

• Simons Center for Geometry & Physic, State University of New York, Stony Brook, USA

  Simon Donaldson

• University of Pennsylvania, Philadelphia, USA

  Eugenio Calabi

Xiuxiong Chen was born in Zhejiang, P. R. China in 1965. His research work is in the area of complex geometry and geometry analysis. Between 2002 and 2009, he was a professor at the University of Wisconsin at Madison, USA.  Since 2009, he has been tenure professor at Stony Brook University.



Simon Donaldson was born in Cambridge, England in 1957. His research work is in the area of differential geometry, with connections to other fields such as topology and algebraic geometry. Between 1985 and 1997 he was a Professor at Oxford University, moving to Imperial College London in 1998. He is currently a permanent member of the Simons Center for Geometry and Physics, Stony Brook University.


Jean-Pierre Bourguignon, born in 1947, is a French mathematician, working in the field of differential geometry. He was president of the Société Mathématique de France from 1990 to 1992. From 1995 to 1998 he was president of the European Mathematical Society. He was director of the Institut des Hautes Études Scientifiques near Paris from 1994 to 2013. From 2014 through 2019 he occupied the post of President of the European Research Council.

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