Abstract:We raise our cups to Urban Cegrell, gone but not forgotten, gone but ever here.Until we meet again in Valhalla!Abstract. With inspiration from the Kähler geometry, we introduce a metric structure on the energy class, E 1,m , of m-subharmonic functions with bounded energy and show that it is complete. After studying how the metric convergence relates to the accepted convergences in this Caffarelli-Nirenberg-Spruck model, we end by constructing geodesics in a subspace of our complete metric space.
“…Cegrell's energy classes can be considered for m-subharmonic functions on domains of C n , 1 ≤ m < n [60,61]. Geodesics for such functions, including the linearity of the corresponding energy functional, were studied in [62].…”
We give a short survey on plurisubharmonic interpolation, with a focus on the possibility of connecting two given plurisubharmonic functions by plurisubharmonic geodesics.
“…Cegrell's energy classes can be considered for m-subharmonic functions on domains of C n , 1 ≤ m < n [60,61]. Geodesics for such functions, including the linearity of the corresponding energy functional, were studied in [62].…”
We give a short survey on plurisubharmonic interpolation, with a focus on the possibility of connecting two given plurisubharmonic functions by plurisubharmonic geodesics.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.