# Properties of Complete Noncompact Warped Product Gradient Yamabe Solitons

## TL;DR

This paper investigates properties of gradient Yamabe solitons on warped product manifolds, providing bounds, estimates, and nonexistence results by adapting maximum principles and Li-Yau techniques.

## Contribution

It introduces new gradient estimates for the warping function and scalar curvature, and establishes a nonexistence theorem for certain gradient Yamabe solitons.

## Key findings

- Lower bounds for potential function and scalar curvature
- Three gradient estimates for the warping function based on scalar curvature sign
- Nonexistence results for specific metric conditions on the base

## Abstract

In this paper, we look for properties of gradient Yamabe solitons on top of warped product manifolds. Utilizing the maximum principle, we find lower bound estimates for both the potential function of the soliton and the scalar curvature of the warped product. By slightly modifying Li-Yau's technique so that we can handle drifting Laplacians, we were able to find three different gradient estimates for the warping function, one for each sign of the scalar curvature of the fiber manifold. As an application, we exhibit a nonexistence theorem for gradient Yamabe solitons possessing certain metric properties on the base of the warped product.