SHAPEFINDERS - A NEW SHAPE DIAGNOSTIC FOR LARGE-SCALE STRUCTURE

We construct a set of shapefinders used to determine the shapes of com pact surfaces (isodensity surfaces in galaxy surveys or N-body simulat ions) without fitting them to ellipsoidal configurations, as has been done earlier. The new indicators, based on the Minkowski functionals, arise from simple, geometrical considerations and are derived from the fundamental properties of a surface such as its volume, surface area, integrated mean curvature, and connectivity characterized by the genu s. These ''shapefinders'' could be used to diagnose the presence of fi laments, pancakes, and ribbons in large-scale structure. Their lower d imensional generalization may be useful for the study of two-dimension al distributions such as temperature maps of the cosmic microwave back ground.