Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
157 tokens/sec
GPT-4o
8 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

A Modified Morrey-Kohn-Hörmander Identity and Applications (1811.03715v2)

Published 8 Nov 2018 in math.CV

Abstract: We prove a modified form of the classical Morrey-Kohn-H\"ormander identity, adapted to pseudoconcave boundaries. Applying this result to an annulus between two bounded pseudoconvex domains in $\mathbb{C}n$, where the inner domain has $\mathcal{C}{1,1}$ boundary, we show that the $L2$ Dolbeault cohomology group in bidegree $(p,q)$ vanishes if $1\leq q\leq n-2$ and is Hausdorff and infinite-dimensional if $q=n-1$, so that the Cauchy-Riemann operator has closed range in each bidegree. As a dual result, we prove that the Cauchy-Riemann operator is solvable in the $L2$ Sobolev space $W1$ on any pseudoconvex domain with $\mathcal{C}{1,1}$ boundary. We also generalize our results to annuli between domains which are weakly $q$-convex in the sense of Ho for appropriate values of $q$.

Summary

We haven't generated a summary for this paper yet.