New type I ancient compact solutions of the Yamabe flow

TL;DR

This paper constructs new rotationally symmetric type I ancient compact solutions to the Yamabe flow that converge to self-similar solutions moving in opposite directions as time approaches negative infinity.

Contribution

It introduces a novel class of ancient solutions to the Yamabe flow that are compact, symmetric, and exhibit specific asymptotic behavior not previously documented.

Findings

Solutions are rotationally symmetric and compact.

Solutions converge to self-similar non-compact solutions as t → -∞.

Solutions are classified as type I ancient solutions.

Abstract

We construct new ancient compact solutions to the Yamabe flow. Our solutions are rotationally symmetric and converge, as $t \to -\infty$, to two self-similar complete non-compact solutions to the Yamabe flow moving in opposite directions. They are type I ancient solutions.