Prefer a chat interface with context about you and your work?
A counterexample to gluing theorems for MCP metric measure spaces
Perelman's doubling theorem asserts that the metric space obtained by gluing along their boundaries two copies of an Alexandrov space with curvature ⩾ κ is an Alexandrov space with the same dimension and satisfying the same curvature lower bound. We show that this result cannot be extended to metric measure …