Bounded Geometry

Bounded geometry is a property of a space or shape that ensures it doesn't become too "wild" or irregular. Specifically, it means that the space has a uniform way of measuring distances and curvature: there is a consistent lower limit on how "spread out" points can be, and an upper limit on how sharply it can bend or curve. This ensures the space is, in a sense, well-behaved everywhere, making it easier to analyze and work with mathematically. Think of it as having a shape that’s smoothly curved without any sudden bumps or infinitely small or large features.