Some Problems On Geometric Function Theory In High Dimensional Spaces

In this paper, we give a new WT-differential form, and obtain its Caccioppoli inequality. Higher integrability results for quasiregular mappings are derived by its corollary. Some new results on Jacobian are obtained by Hodge decomposition. The paper is composed of 5 chap-ters:The first chapter is an introduction; the second chapter outlines the preliminary lemmas; the third chapter gives a definition of WT class of differential forms, and obtain its Caccioppoli inequality; in the forth chapter, some new results on Jacobian are obtained; in the last chatper, Chapter V, we list the main conclusions of this paper.