SOME PROBLEMS OF MASS GEOMETRY IN THE CASE OF SIGNED DENSITY
In this paper we consider and solve the following problems of mass geometry for signed density: the criterion for existence of a center of mass in the case of zero mass, theorem on moment of inertia with respect to plane parallel sets, determination of the inertia surface (similarity to the inertia ellipsoid in the case of the positive density), examples of empty inertia surfaces, the criterion for existence of a point whose inertia surface is a sphere or an empty set, the problem of construction of an inertia surface at an arbitrary point with known central inertia surface and others.