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math.MG2026
Hadwiger's classification theorem on the sphere via signed orthoscheme decompositions
Martin Lotz
We give an elementary and combinatorial proof of the spherical Hadwiger theorem, which states that every continuous, rotation-invariant valuation on the space of closed convex cone…
math.MG2026
Monotone invariant valuations on convex cones
Martin Lotz
We classify the monotone $\SOn d$-invariant valuations, , on the space of all closed convex cones. They are precisely the linear combinations of the conic intrinsic volumes…