# Escobar constants of planar domains

## TL;DR

This paper introduces the concept of higher-order Escobar constants for bounded planar domains, providing explicit calculations for the unit disk and certain polygons, advancing understanding in geometric analysis.

## Contribution

It is the first to study higher-order Escobar constants on planar domains and computes these constants for specific shapes like the disk and polygons.

## Key findings

- Explicit formulas for $I_k$ on the unit disk.
- Computed $I_k$ for a family of polygons.
- Established foundational results for higher-order Escobar constants.

## Abstract

We initiate the study of the higher-order Escobar constants $I_k(M)$, $k\geq 3$, on bounded planar domains $M$. The Escobar constants $I_k$ of the unit disk and a family of polygons are provided.