2022/01/28 by Lempert, László
#32Q15 #32U15 #53C35 #58B20 #58E30 #70H99 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2201.12445
Consider a compact Kähler manifold (X,ω) and the space \cal E(X,ω)=\cal E of ω--plurisubharmonic functions of full Monge--Ampère mass on it. We introduce a quantity ρ[u,v] to measure the distance between u, v∈\cal E; ρ[u,v] is not a number but rather a decreasing function on a certain interval (0,V)⊂\mathbb R. We explore properties of ρ[u,v], and using them we study Lagrangians and associated energy spaces of ω--plurisubharmonic functions. Many results here generalize Darvas's findings about his metrics dχ.