Luis Santaló – Neglected Science

Lluis Antoni Santaló Sors, Spanish-born Argentine geometer (Girona, Catalunya 09 October 1911 – Buenos Aires 22 November 2001)

Regarded internationally as founder of modern integral geometry and one of greatest geometers of the 20^th century

Authored over 150 papers

Authored 25 books between them Vectores y Tensores (1961) and Integral Geometry and Geometric Probabilities (1976)

Invited Lecturer, International Congress of Mathematicians (1950)

With Chern regarded as founder of hyperbolic integral geometry

Introduced kinetic density for sets of geodesies on two-dimensional surfaces

Introduced affine unimodular invariant (1958)

Obtained integral formulas for a two-dimensional Riemannian space of negative constant curvature

Laid the mathematical foundations for the creation of stereology

Introduced convex sets by horospheres

Proposed a definition for absolute total curvatures of a Euclidean space closed subset

Solved the problem of one-dimensional foliations in a Riemann variety

A new affine invariant plane and solid convex bodies. Math Notae 16:78-91, 1958

Some integral formulas and a definition of q-dimensional area for a set of points. Rev. Univ. Nac. Tucumán 7:271-82, 1950

An affine invariant for convex bodies in n-dimensional space. Portugaliae Math. 8:155-61, 1949

An affine invariant for closed convex plane curves. Math. Notae 8:103-11, 1948

Some integral formulas referring to convex bodies. Rev. Un. Mat. Arg. 12:78-87, 1946

A theorem on conformal mapping. Math. Notae 5:29-40, 1945

An integral formula concerning convex figures. Rev. Uni. Mat. Argentina 8:165-91, 1942

A theorem and an inequality referring to rectificable curves. Amer. J. Math. 63:635-44, 1941

A theorem on sets of parallelepipeds with parallel edges. Publ. Inst. Mat. Univ. Nac. Litoral 2:49-60, 1940

Blaschke-Santaló inequality

Blaschke-Chern-Santaló theorem

Santaló bodies

Santaló conjecture on convex sets

Santaló K point

Santaló point of a function

Santaló formula

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