# Sharp Vanishing order of solutions to Stationary Schrodinger equations on Carnot groups of arbitrary step

## TL;DR

This paper establishes an optimal upper bound on the vanishing order of solutions to stationary Schrödinger equations on Carnot groups, extending strong unique continuation principles to sub-Laplacians of arbitrary step.

## Contribution

It introduces a novel frequency function approach to derive sharp vanishing order bounds for Schrödinger equations on general Carnot groups, generalizing previous Euclidean results.

## Key findings

- Proves an optimal vanishing order bound for solutions.
- Provides a quantitative form of strong unique continuation.
- Extends results to Carnot groups of arbitrary step.

## Abstract

Based on a variant of the frequency function approach of Almgren([Al]), we establish an optimal upper bound on the vanishing order of solutions to stationary Schr\"odinger equations associated to sub-Laplacian on Carnot groups of arbitrary step. Such bound provides a quantitative form of strong unique continuation and can be thought of as an analogue of the recent results of Bakri and Zhu for the standard Laplacian.