New Results on Plurisubharmonic Functions in Complex Analysis

Introduction

In complex analysis, plurisubharmonic functions play a significant role in the study of various geometric and analytic properties of complex domains. They are closely related to the concept of pseudoconvexity, an essential aspect of the theory of functions of several complex variables.

Recent Developments

Recent years have witnessed significant advancements in the study of plurisubharmonic functions. Mathematicians have developed new techniques and refined existing ones to gain deeper insights into their behavior and applications. One of the most notable breakthroughs is the construction of strictly plurisubharmonic exhaustion functions for arbitrary relatively compact pseudoconvex domains with smooth boundaries.

These developments have opened up new avenues for research in several areas, including geometric function theory, complex differential geometry, and the theory of holomorphic functions. They have also led to a better understanding of the structure and properties of complex domains.

Conclusion

The ongoing research on plurisubharmonic functions continues to yield fascinating results and expand our knowledge of complex analysis. As mathematicians continue to explore this field, we can expect further groundbreaking discoveries in the years to come.