A note on the long neck principle and spectral width inequality of geodesic collar neighborhoods

Abstract

The main purpose of this short note is to derive some generalizations of the long neck principle and give a spectral width inequality of geodesic collar neighborhoods. Our results are obtained via the spinorial Callias operator approach. An important step is to introduce the relative Gromov-Lawson pair on a compact manifold with boundary, relative to a background manifold.

Final version, to appear in the Proceedings of the American Mathematical Society

References in corpus (3)

• Boundary conditions for scalar curvature
• Metrics with ${\lambda }_1(-\Delta +kR)\ge 0$ and flexibility in the Riemannian Penrose Inequality
• Spectral Torical Band Inequalities and Generalizations of the Schoen-Yau Black Hole Existence Theorem

Cited by in corpus (1)

• The odd-dimensional long neck problem via spectral flow