# Conformal invariants from nodal sets II. Manifolds with boundary

## TL;DR

This paper investigates conformal invariants derived from nodal sets and eigenvalues of conformally covariant operators on manifolds with boundary, extending previous work and applying to curvature prescription problems.

## Contribution

It introduces a general framework for boundary operators of arbitrary order and relates Dirichlet and Neumann eigenvalues in the context of conformal invariants.

## Key findings

- Established relations between Dirichlet and Neumann eigenvalues.
- Extended conformal invariant analysis to manifolds with boundary.
- Applied results to curvature prescription problems.

## Abstract

In this paper, we study conformal invariants that arise from nodal sets and negative eigenvalues of conformally covariant operators on manifolds with boundary. We also consider applications to curvature prescription problems on manifolds with boundary. We relate Dirichlet and Neumann eigenvalues and put the results developed here for the Escobar problem into the more general framework of boundary operators of arbitrary order.