Weighted boundary limits of the generalized Kobayashi-Royden metrics on weakly pseudoconvex domains

Abstract

The purpose of this paper is to study the existence of weighted boundary limits of the generalized Kobayashi-Royden metrics on weakly pseudoconvex domains in <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper C Superscript n"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">C</mml:mi> </mml:mrow> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> <mml:annotation encoding="application/x-tex">{\mathbb {C}^n}</mml:annotation> </mml:semantics> </mml:math> </inline-formula> and to explore the connections between the limits and the Levi invariants. The main result extends Graham’s result on strongly pseudoconvex domains to a large class of weakly pseudoconvex domains.