Toshiki Mabuchi

Toshiki Mabuchi (kanji: 満渕俊樹, hiragana: マブチ トシキ, Mabuchi Toshiki, born in 1950) is a Japanese mathematician, specializing in complex differential geometry and algebraic geometry. In 2006 in Madrid he was an invited speaker at the International Congress of Mathematicians. Mabuchi is known for introducing the Mabuchi functional.

Education and career In 1972 Mabuchi graduated from the University of Tokyo Faculty of Science There he graduated with a Ph.D. in 1977 with thesis C3-Actions and Algebraic Threefolds with Ample Tangent Bundle and advisor Shoshichi Kobayashi As a postdoc Mabuchi was from 1977 to 1978 a guest researcher at the University of Bonn. Since 1978 he is a faculty member of the Department of Mathematics of Osaka University. His research deals with complex differential geometry, extremal Kähler metrics, stability of algebraic varieties, and the Hitchin–Kobayashi correspondence. The Futaki invariant and Mabuchi energy are fundamental in understanding obstructions to the existence of Kähler metrics which are Einstein or which have constant scalar curvature.

A year later, by use of the -lemma, Mabuchi considered a natural Riemannian metric on a Kähler class, which allowed him to define length, geodesics, and curvature; the sectional curvature of Mabuchi's metric is nonpositive. Along geodesics in the Kähler class, the Mabuchi energy is convex. So the Mabuchi energy has strong variational properties.

Selected publications Articles

Books