In this article, we use the second intrinsic volume to define a metric on the space of
homothetic classes of Gaussian bounded convex bodies in a separable real Hilbert space.
Using kernels of hyperbolic type, we can deduce that this space is isometrically embedded
into an infinite-dimensional real hyperbolic space. Applying Malliavin calculus, it is possible
to adapt integral geometry for convex bodies in infinite dimensions. Moreover, we give a
new formula for computing second intrinsic volumes of convex bodies and offer a description …

In this article, we use the second intrinsic volume to define a kernel of hyperbolic type on the
space of homothety classes of Gaußian bounded convex bodies in a separable real Hilbert
space. With this kernel, we deduce that this space can be embedded into an infinite-
dimensional real hyperbolic space and is then equipped with a hyperbolic metric, which is
the “area distance” introduced by Debin and Fillastre (Gr Geom Dyn 16 (1): 115–140, 2022).
Applying the Malliavin calculus, it is possible to adapt integral geometry for convex bodies in …