The isoperimetric constant is a numerical value that measures the efficiency of a shape in enclosing volume with respect to its surface area. It is defined for a domain in a metric space and can be thought of as a comparison between the shape's perimeter (or surface area) and its enclosed volume. A higher isoperimetric constant indicates that a shape is more efficient in enclosing volume relative to its boundary, often leading to important implications in various mathematical areas including analysis and geometry.
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