Christos Saroglou

MORE ON LOGARITHMIC SUMS OF CONVEX BODIES

We prove that the log-Brunn-Minkowski inequality (log-BMI) for the Lebesque measure in dimension

VOLUMES OF PROJECTION BODIES OF SOME CLASSES OF CONVEX BODIES

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Characterizations of Extremals for some Functionals on Convex Bodies

would imply the log-BMI and, therefore, the B-conjecture for any log-concave density in dimension

Characterization of Simplices via the Bezout Inequality for Mixed Volumes

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Remarks on the conjectured log-Brunn–Minkowski inequality

. As a consequence, we prove the log-BMI and the B-conjecture for any log-concave density, in the plane. Moreover, we prove that the log-BMI reduces to the following: For each dimension

Estimating volume and surface area of a convex body via its projections or sections

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Iterations of the projection body operator and a remark on Petty's conjectured projection inequality

, there is a density

Minimal surface area position of a convex body is not always an M-position

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Shadow systems: remarks and extensions

, which satisfies an integrability assumption, so that the log-BMI holds for parallelepipeds with parallel facets, for the density

On the Equivalence Between Two Problems of Asymmetry on Convex Bodies

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