Toshiki Mabuchi

In 2006 Toshiki Mabuchi and Takashi Shioya received the Geometry Prize of the Mathematical Society of Japan.

Mabuchi is well-known for his introduction, in 1986, of the Mabuchi energy, which gives a variational interpretation to the problem of Kähler metrics of constant scalar curvature. In particular, the Mabuchi energy is a real-valued function on a Kähler class whose Euler-Lagrange equation is the constant scalar curvature equation. In the case that the Kähler class represents the first Chern class of the complex manifold, one has a relation to the Kähler-Einstein problem, due to the fact that constant scalar curvature metrics in such a Kähler class must be Kähler-Einstein.

In 1972 Mabuchi graduated from the University of Tokyo Faculty of Science and became a graduate student in mathematics at the University of California, Berkeley. 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.

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.