the Calabi flow is a geometric flow which deforms a Kähler metric on a complex manifold. Precisely, given a Kähler manifold M, the Calabi flow is given...

Eugenio Calabi (May 11, 1923 – September 25, 2023) was an Italian-born American mathematician and the Thomas A. Scott Professor of Mathematics at the University...

uniformization theorem Calabi flow, a flow for Kähler metrics Yamabe flow Important classes of flows are curvature flows, variational flows (which extremize...

class [ ω ] {\displaystyle [\omega ]} . Understanding the flow of this functional, the Calabi flow, is a key goal in understanding the existence of canonical...

solutions of Calabi flow on surfaces of genus h ≥ 2", J. Math. Kyoto Univ., 40 (2): 363–377, doi:10.1215/kjm/1250517718 Brendle, Simon (2010), Ricci flow and the...

equation Calabi flow in the study of Calabi-Yau manifolds Cauchy–Riemann equations Equations for a minimal surface Liouville's equation Ricci flow, used...

bladder cancer. Eugenio Calabi, 100, Italian-born American mathematician (Calabi conjecture, Calabi–Yau manifold, Calabi flow). Bob Dahl, 54, American...

recognition of his contributions to partial differential equations, the Calabi conjecture, the positive energy theorem, and the Monge–Ampère equation....

Phase separation Calabi flow Any ∂ g i j ∂ t = ( Δ R ) g i j {\displaystyle {\frac {\partial g_{ij}}{\partial t}}=(\Delta R)g_{ij}} Calabi–Yau manifolds...

facts label) (b. 1947) Eugenio Calabi, 100, Italian-born mathematician (Calabi conjecture, Calabi–Yau manifold, Calabi flow) (b. 1923) Gerry Shamray, 66...

Ricci flow in the setting of Kähler manifolds. In his Ph.D. thesis, published in 1985, he showed that Yau's estimates in the resolution of the Calabi conjecture...

Kähler–Einstein metric. The most important special case of these are the Calabi–Yau manifolds, which are Kähler and Ricci-flat. The most important problem...

physics, the compact extra dimensions must be shaped like a Calabi–Yau manifold. A Calabi–Yau manifold is a special space which is typically taken to...

Kähler-Einstein metrics. Shing-Tung Yau, in his renowned resolution of the Calabi conjecture, had settled the case of closed Kähler manifolds with nonpositive...

program) Cadarache Caesar Saloma Cahn–Hilliard equation Calabi flow Calabi–Yau four-fold Calabi–Yau manifold Calandria (disambiguation), three different...

in mathematics to solve problems such as the Poincaré conjecture and the Calabi conjecture. They are difficult to study: almost no general techniques exist...

that mirror to a symplectic manifold (which is a Calabi–Yau manifold) there should be another Calabi–Yau manifold for which the symplectic structure is...

conjecture. Namely the use of the Kähler–Ricci flow as an analogy of the Yang–Mills flow, and of the Calabi functional and K-energy functional in comparison...

Hausdorff space Almost complex manifold Algebraic manifold Analytic manifold Calabi–Yau manifold Complex manifold, a manifold over the complex numbers Differentiable...

theory in theoretical physics. Thomas obtained his PhD on gauge theory on Calabi–Yau manifolds in 1997 under the supervision of Simon Donaldson at the University...

\mathrm {d} f)={\text{Crit}}(f)} . In the case of Kähler manifolds (or Calabi–Yau manifolds) we can make a choice Ω = Ω 1 + i Ω 2 {\displaystyle \Omega...

quantization by Nathan Berkovits. Nigel Hitchin introduced generalized Calabi–Yau manifolds, where the generalized complex structure is defined by a pure...

that these theories are related by a renormalization group flow to sigma models on Calabi–Yau manifolds. In his 1993 paper "Phases of N = 2 theories in...

Hermitian manifold Newlander–Nirenberg theorem Generalized complex manifold Calabi–Yau manifold Hyperkähler manifold K3 surface hypercomplex manifold Quaternion-Kähler...

Irvine) - Generalized Kahler Ricci flow and a generalized Calabi conjecture Jean-Pierre Bourguignon (IHES) Eugenio Calabi (Penn) Yakov Eliashberg (Stanford)...

Locally Simply Connected". Ann. of Math. (2) 160 (2004), no. 1, 573–615. "The Calabi-Yau Conjectures for Embedded Surfaces", Ann. of Math. (2) 167 (2008), no...

homology of Lagrangians in a Calabi–Yau manifold X {\displaystyle X} and the Ext groups of coherent sheaves on the mirror Calabi–Yau manifold. In this situation...

Camerino & Calabi 1991, p. 108. Concina, Camerino & Calabi 1991, pp. 108–109. Concina, Camerino & Calabi 1991, p. 161. Concina, Camerino & Calabi 1991, p...

polyhedron models Jean-Louis Koszul (1921–2018) Isaak Yaglom (1921–1988) Eugenio Calabi (1923–2023) Benoit Mandelbrot (1924–2010) – fractal geometry Katsumi Nomizu...

transcendental bijection of the spacetime continuum, an asymptotic projection of the Calabi–Yau manifold manifesting itself in anti-de Sitter space. Wormholes are consistent...