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      Brunn-Minkowski and Zhang inequalities for convolution bodies 

      Alonso Gutiérrez, David; Jiménez Gómez, Carlos Hugo; Villa Caro, Rafael (Elsevier, 2013-05-01)
      A quantitative version of Minkowski sum, extending the definition of θ-convolution of convex bodies, is studied to obtain ...
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      John's ellipsoid and the integral ratio of a log-concave function 

      Alonso Gutiérrez, David; González Merino, Bernardo; Jiménez Gómez, Carlos Hugo; Villa Caro, Rafael (Springer, 2018-04)
      We extend the notion of John’s ellipsoid to the setting of integrable log-concave functions. This will allow us to define ...
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      Rogers-Shephard inequality for log-concave functions 

      Alonso Gutiérrez, David; González Merino, Bernardo; JIménez Gömez, Carlos Hugo; Villa Caro, Rafael (Elsevier, 2016-12-01)
      In this paper we prove different functional inequalities extending the classical Rogers-Shephard inequalities for convex ...
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      Volume inequalities for the i-th-convolution bodies 

      Alonso Gutiérrez, David; González Merino, Bernardo; Jiménez Gómez, Carlos Hugo (Elsevier, 2015-04-01)
      We obtain a new extension of Rogers-Sephard inequality providing an upper bound for the volume of the sum of two convex ...