Kinematic formulas for mean curvature powers of hypersurfaces and Hadwiger’s theorem in 𝑅²ⁿ
Kinematic formulas for mean curvature powers of hypersurfaces and Hadwiger’s theorem in 𝑅²ⁿ
We first discuss the theory of hypersurfaces and submanifolds in the <italic>m</italic>-dimensional Euclidean space leading up to high dimensional analogues of the classical Euler’s and Meusnier’s theorems. Then we deduce the kinematic formulas for powers of mean curvature of the <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="left-parenthesis m minus 2 right-parenthesis"> <mml:semantics> …