Boundary flexibility for curvature conditions
Abstract
We prove a general boundary gluing principle for families of Riemannian metrics with pointwise curvature restrictions on manifolds with possibly non-compact boundary. This includes, as special cases, the classical gluing theorems by Perelman for metrics with positive Ricci curvature and convex singularities and by Gromov-Lawson and Bär-Hanke for metrics with positive scalar curvature and mean convex singularities. Using the language of algebraic curvature cones, our theorem implies and unifies many more previous gluing results. We also prove a boundary deformation principle that enables us to compare spaces of metrics with interior curvature restrictions and different boundary conditions. Our construction is based on the local flexibility lemma for open partial differential relations, as well as explicit 1-jet deformations of metrics along the boundary.
Related
- Asymptotic Dynamics of Forced Curvature Flow in a Planar Strip with Robin Boundary Conditions
- Radial Powered Mean Curvature Flow with Robin Boundary Conditions
- Rigidity and flexibility under positive isotropic curvature
- Constant mean curvature disks with circular boundary
- Constant mean curvature disks with circular boundary in the $3$-sphere and in hyperbolic space
BibTeX
@misc{frerichs2026boundary,
title = {{Boundary flexibility for curvature conditions}},
author = {Helge Frerichs},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.14581},
eprint = {2609.14581},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14581},
}
RIS
TY - UNPB
TI - Boundary flexibility for curvature conditions
AU - Helge Frerichs
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2609.14581
UR - https://arxiv.org/abs/2609.14581
AB - We prove a general boundary gluing principle for families of Riemannian metrics with pointwise curvature restrictions on manifolds with possibly non-compact boundary. This includes, as special cases, the classical gluing theorems by Perelman for metrics with positive Ricci curvature and convex singularities and by Gromov-Lawson and Bär-Hanke for metrics with positive scalar curvature and mean convex singularities. Using the language of algebraic curvature cones, our theorem implies and unifies many more previous gluing results. We also prove a boundary deformation principle that enables us to compare spaces of metrics with interior curvature restrictions and different boundary conditions. Our construction is based on the local flexibility lemma for open partial differential relations, as well as explicit 1-jet deformations of metrics along the boundary.
ER -