# Connected sum of CR manifolds with positive CR Yamabe constant

## TL;DR

This paper proves that the connected sum of two 3-dimensional closed CR manifolds with positive CR Yamabe constants also admits a CR structure with a positive CR Yamabe constant, extending the class of such manifolds.

## Contribution

It demonstrates that the property of having a positive CR Yamabe constant is preserved under the connected sum operation for 3-dimensional CR manifolds.

## Key findings

- Connected sum of two CR manifolds with positive CR Yamabe constant also has positive CR Yamabe constant.
- Extends the class of CR manifolds known to admit positive CR Yamabe structures.
- Provides a method to construct new CR manifolds with positive CR Yamabe constant from existing ones.

## Abstract

Suppose $M_{1}$ and $M_{2}$ are $3$-dimensional closed (compact without boundary) CR manifolds with positive CR Yamabe constant. In this note, we show that the connected sum of $M_{1}$ and $M_{2}$ also admits a CR structure with positive CR Yamabe constant.