Generalized stationary discs attached to degenerate submanifolds in $\mathbb{C}^N$

TL;DR

This paper investigates the structure of generalized stationary discs attached to Levi degenerate submanifolds in complex space, showing under certain conditions that they form a finite-dimensional real submanifold.

Contribution

It establishes the finite-dimensionality of the family of stationary discs attached to Levi degenerate submanifolds under specific geometric assumptions.

Findings

Family of stationary discs forms a finite-dimensional real submanifold

Results apply to Levi degenerate submanifolds in complex space

Provides geometric conditions for the structure of stationary discs

Abstract

We study the family of generalized stationary discs attached to a Levi degenerate submanifold M of codimension d in $\mathbb{C}^{n+d}$. We show, under suitable geometric assumptions on M, that this family forms a finite dimensional real submanifold of the Banach space of analytic discs.