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Erwin Lutwak

Full Professor Mathematics

    1975 …2019
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    Research Output 1975 2019

    • 74 Article
    • 5 Chapter (peer-reviewed)
    • 1 Editorial
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    Article
    2019

    The dual Minkowski problem for symmetric convex bodies

    Böröczky, K. J., Lutwak, E., Yang, D., Zhang, G. & Zhao, Y., Nov 7 2019, In : Advances in Mathematics. 356, 106805.

    Research output: Contribution to journalArticle

    Convex Body
    Entropy
    Curvature Measure
    Estimate
    Necessary Conditions
    2018

    Lp dual curvature measures

    Lutwak, E., Yang, D. & Zhang, G., Apr 30 2018, In : Advances in Mathematics. 329, p. 85-132 48 p.

    Research output: Contribution to journalArticle

    Curvature Measure
    Mixed Volume
    Surface area
    Curvature
    Borel Measure

    The LP-Aleksandrov problem for LP-integral curvature

    Huang, Y., Lutwak, E., Yang, D. & Zhang, G., Sep 1 2018, In : Journal of Differential Geometry. 110, 1, p. 1-29 29 p.

    Research output: Contribution to journalArticle

    Curvature
    Convex Body
    Necessary Conditions
    Sufficient Conditions
    2017

    The dual Minkowski problem for symmetric convex bodies

    Böröczky, K. J., Lutwak, E., Yang, D., Zhang, G. & Zhao, Y., Mar 18 2017, In : arXiv.

    Research output: Contribution to journalArticle

    Convex Body
    Curvature Measure
    Unit Sphere
    Necessary Conditions
    Sufficient Conditions
    2016

    Geometric measures in the dual Brunn–Minkowski theory and their associated Minkowski problems

    Huang, Y., Lutwak, E., Yang, D. & Zhang, G., Jun 1 2016, In : Acta Mathematica. 216, 2, p. 325-388 64 p.

    Research output: Contribution to journalArticle

    Curvature Measure
    Convex Body
    Sufficient Conditions
    Borel Measure
    Existence of Solutions
    2015

    Affine images of isotropic measures

    Böröczky, K. J., Lutwak, E., Yang, D. & Zhang, G., Mar 1 2015, In : Journal of Differential Geometry. 99, 3, p. 407-442 36 p.

    Research output: Contribution to journalArticle

    Isoperimetric Inequality
    Borel Measure
    Reverse
    Convex Body
    Euclidean
    2014

    A unified approach to Cramér-rao inequalities

    Cianchi, A., Lutwak, E., Yang, D. & Zhang, G., Jan 2014, In : IEEE Transactions on Information Theory. 60, 1, p. 643-650 8 p., 6655985.

    Research output: Contribution to journalArticle

    Random variables
    Boundary conditions
    2013

    Affine Moments of a Random Vector

    Lutwak, E., Lv, S., Yang, D. & Zhang, G., 2013, In : IEEE Transactions on Information Theory. 59, 9, p. 5592-5599 8 p., 6524015.

    Research output: Contribution to journalArticle

    entropy
    Entropy

    The logarithmic Minkowski problem

    Böröczky, K. J., Lutwak, E., Yang, D. & Zhang, G., 2013, In : Journal of the American Mathematical Society. 26, 3, p. 831-852 22 p.

    Research output: Contribution to journalArticle

    Banach spaces
    Cones
    Logarithmic
    Unit Sphere
    Unit ball
    2012

    Extensions of fisher information and stam's inequality

    Lutwak, E., Lv, S., Yang, D. & Zhang, G., Mar 2012, In : IEEE Transactions on Information Theory. 58, 3, p. 1319-1327 9 p., 6157091.

    Research output: Contribution to journalArticle

    Fisher information matrix
    entropy
    Random variables
    Entropy

    The Brunn-Minkowski-Firey inequality for nonconvex sets

    Lutwak, E., Yang, D. & Zhang, G., Feb 2012, In : Advances in Applied Mathematics. 48, 2, p. 407-413 7 p.

    Research output: Contribution to journalArticle

    Brunn-Minkowski Inequality
    Convex Body
    Compact Set
    Euclidean space
    Equality

    The log-Brunn-Minkowski inequality

    Böröczky, K. J., Lutwak, E., Yang, D. & Zhang, G., Oct 2012, In : Advances in Mathematics. 231, 3-4, p. 1974-1997 24 p.

    Research output: Contribution to journalArticle

    Brunn-Minkowski Inequality
    Convex Body
    Mixed Volume
    Unit ball
    Banach space
    2011

    A countable set of directions is sufficient for Steiner symmetrization

    Bianchi, G., Klain, D. A., Lutwak, E., Yang, D. & Zhang, G., Oct 2011, In : Advances in Applied Mathematics. 47, 4, p. 869-873 5 p.

    Research output: Contribution to journalArticle

    Symmetrization
    Countable
    Sufficient
    2010

    A volume inequality for polar bodies

    Lutwak, E., Yang, D. & Zhang, G., Jan 2010, In : Journal of Differential Geometry. 84, 1, p. 163-178 16 p.

    Research output: Contribution to journalArticle

    Isoperimetric Inequality
    Equality
    Lower bound
    If and only if

    Orlicz centroid bodies

    Lutwak, E., Yang, D. & Zhang, G., Feb 2010, In : Journal of Differential Geometry. 84, 2, p. 365-387 23 p.

    Research output: Contribution to journalArticle

    Centroid
    Star Body
    Analogue
    Isoperimetric Inequality
    Convex Body

    Orlicz projection bodies

    Lutwak, E., Yang, D. & Zhang, G., Jan 15 2010, In : Advances in Mathematics. 223, 1, p. 220-242 23 p.

    Research output: Contribution to journalArticle

    Projection
    Analogue

    The even Orlicz Minkowski problem

    Haberl, C., Lutwak, E., Yang, D. & Zhang, G., Aug 2010, In : Advances in Mathematics. 224, 6, p. 2485-2510 26 p.

    Research output: Contribution to journalArticle

    2009

    Affine Moser-trudinger and Morrey-sobolev inequalities

    Cianchi, A., Lutwak, E., Yang, D. & Zhang, G., Oct 2009, In : Calculus of Variations and Partial Differential Equations. 36, 3, p. 419-436 18 p.

    Research output: Contribution to journalArticle

    Sobolev Inequality
    Moser-Trudinger Inequality
    Energy
    Gradient
    Geometric Inequalities
    2007

    Moment-entropy inequalities for a random vector

    Lutwak, E., Yang, D. & Zhang, G., Apr 2007, In : IEEE Transactions on Information Theory. 53, 4, p. 1603-1607 5 p.

    Research output: Contribution to journalArticle

    entropy
    Entropy
    Covariance matrix

    Volume inequalities for isotropic measures

    Lutwak, E., Yang, D. & Zhang, G., Dec 2007, In : American Journal of Mathematics. 129, 6, p. 1711-1723 13 p.

    Research output: Contribution to journalArticle

    Ball
    Arbitrary
    Equality
    2006

    Optimal Sobolev norms and the Lp Minkowski problem

    Lutwak, E., Yang, D. & Zhang, G., 2006, In : International Mathematics Research Notices. 2006, p. 1-21 21 p.

    Research output: Contribution to journalArticle

    Norm
    2005
    entropy
    Entropy
    Random variables

    Lp John ellipsoids

    Lutwak, E., Yang, D. & Zhang, G., 2005, In : Proceedings of the London Mathematical Society. 90, 2, p. 497-520 24 p.

    Research output: Contribution to journalArticle

    Ellipsoid

    On the Lp minkowski problem for polytopes

    Hug, D., Lutwak, E., Yang, D. & Zhang, G., 2005, In : Discrete and Computational Geometry. 33, 4, p. 699-715 17 p.

    Research output: Contribution to journalArticle

    Discrete Data
    Polytopes
    Existence of Solutions
    2004

    A generalized affine isoperimetric inequality

    Chen, W., Howard, R., Lutwak, E., Yang, D. & Zhang, G., 2004, In : Journal of Geometric Analysis. 14, 4, p. 597-612 16 p.

    Research output: Contribution to journalArticle

    Isoperimetric Inequality
    Convex Geometry
    Affine geometry
    Differential Geometry

    Moment-entropy inequalities

    Lutwak, E., Yang, D. & Zhang, G., Jan 2004, In : Annals of Probability. 32, 1 B, p. 757-774 18 p.

    Research output: Contribution to journalArticle

    Moment Inequalities
    Entropy Inequality
    Random Vector
    Isoperimetric Inequality
    Expected Value

    On the Lp-Minkowski problem

    Lutwak, E., Yang, D. & Zhang, G., Nov 2004, In : Transactions of the American Mathematical Society. 356, 11, p. 4359-4370 12 p.

    Research output: Contribution to journalArticle

    Formulation

    Volume inequalities for subspaces of Lp

    Lutwak, E., Yang, D. & Zhang, G., Sep 2004, In : Journal of Differential Geometry. 68, 1, p. 159-184 26 p.

    Research output: Contribution to journalArticle

    Reverse Inequality
    Isoperimetric Inequality
    Unit ball
    Ball
    Uniqueness
    2002

    Information-theoretic inequalities for contoured probability distributions

    Guleryuz, O. G., Lutwak, E., Yang, D. & Zhang, G., Aug 2002, In : IEEE Transactions on Information Theory. 48, 8, p. 2377-2383 7 p.

    Research output: Contribution to journalArticle

    Probability distributions
    Entropy
    entropy

    Sharp affine Lp Sobolev inequalities

    Lutwak, E., Yang, D. & Zhang, G., Sep 2002, In : Journal of Differential Geometry. 62, 1, p. 17-38 22 p.

    Research output: Contribution to journalArticle

    Sobolev Inequality
    Conformal Structure
    Lebesgue Measure
    Scalar, inner or dot product
    Affine transformation

    The Cramer-Rao inequality for star bodies

    Lutwak, E., Yang, D. & Zhang, G., Mar 15 2002, In : Duke Mathematical Journal. 112, 1, p. 59-81 23 p.

    Research output: Contribution to journalArticle

    Cramér-Rao Inequality
    Star Body
    Ellipsoid
    Legendre
    Star-shaped Set
    2001
    Affine Invariant
    Isoperimetric Inequality
    Polytopes
    Projection
    Reverse Inequality
    2000

    A new ellipsoid associated with convex bodies

    Lutwak, E., Yang, D. & Zhang, G., Sep 15 2000, In : Duke Mathematical Journal. 104, 3, p. 375-390 16 p.

    Research output: Contribution to journalArticle

    Convex Body
    Ellipsoid

    Lp affine isoperimetric inequalities

    Lutwak, E., Yang, D. & Zhang, G., Sep 2000, In : Journal of Differential Geometry. 56, 1, p. 111-132 22 p.

    Research output: Contribution to journalArticle

    Isoperimetric Inequality
    Centroid
    Projection
    Analogue
    1998

    Containment and circumscribing simplices

    Lutwak, E., 1998, In : Discrete and Computational Geometry. 19, 2, p. 229-235 7 p.

    Research output: Contribution to journalArticle

    Mixed Volume
    Convex Body
    Theorem
    1997

    Blaschke-Santaló inequalities

    Lutwak, E. & Zhang, G., Sep 1997, In : Journal of Differential Geometry. 47, 1, p. 1-16 16 p.

    Research output: Contribution to journalArticle

    Bodies with similar projections

    Chakerian, G. D. & Lutwak, B., 1997, In : Transactions of the American Mathematical Society. 349, 5, p. 1811-1820 10 p.

    Research output: Contribution to journalArticle

    Convex Body
    Projection
    Subspace
    Mixed Volume
    Orthogonal Projection

    Inequalities for Mean Circumscribing Simplices

    Lutwak, E., 1997, In : Geometriae Dedicata. 66, 1, p. 119-124 6 p.

    Research output: Contribution to journalArticle

    Convex Body
    Generalise
    1996

    Functional analytic characterizations of classes of convex bodies

    Goodey, P., Lutwak, E. & Weil, W., Jul 1996, In : Mathematische Zeitschrift. 222, 3, p. 363-381 19 p.

    Research output: Contribution to journalArticle

    Convex Body
    Class

    The Brunn-Minkowski-Firey theory II: Affine and geominimal surface areas

    Lutwak, E., Mar 25 1996, In : Advances in Mathematics. 118, 2, p. 244-294 51 p.

    Research output: Contribution to journalArticle

    Surface area
    1995

    On the regularity of solutions to a generalization of the Minkowski problem

    Lutwak, E. & Oliker, V., Jan 1995, In : Journal of Differential Geometry. 41, 1, p. 227-246

    Research output: Contribution to journalArticle

    1993

    A Minimax Inequality for Inscribed Cones

    Lutwak, E., Jun 1993, In : Journal of Mathematical Analysis and Applications. 176, 1, p. 148-155 8 p.

    Research output: Contribution to journalArticle

    Minimax Inequality
    Cones
    Cone

    Inequalities for mixed projection bodies

    Lutwak, E., Oct 1993, In : Transactions of the American Mathematical Society. 339, 2, p. 901-916

    Research output: Contribution to journalArticle

    The brunn-minkowski-firey theory I: Mixed volumes and the minkowski problem

    Lutwak, E., 1993, In : Journal of Differential Geometry. 38, 1, p. 131-150 20 p.

    Research output: Contribution to journalArticle

    Mixed Volume
    1992

    On the semicontinuity of curvatures

    Lutwak, E., Dec 1992, In : Commentarii Mathematici Helvetici. 67, 1, p. 664-669 6 p.

    Research output: Contribution to journalArticle

    Semicontinuity
    Curvature
    1991

    Extended affine surface area

    Lutwak, E., 1991, In : Advances in Mathematics. 85, 1, p. 39-68 30 p.

    Research output: Contribution to journalArticle

    Surface area
    Ellipsoid
    1990

    Centroid bodies and dual mixed volumes

    Lutwak, E., 1990, In : Proceedings of the London Mathematical Society. s3-60, 2, p. 365-391 27 p.

    Research output: Contribution to journalArticle

    Mixed Volume
    Centroid

    On Quermassintegrals of mixed projection bodies

    Lutwak, E., Jan 1990, In : Geometriae Dedicata. 33, 1, p. 51-58 8 p.

    Research output: Contribution to journalArticle

    Projection
    Convex Body
    Convexity
    Family
    1988

    Inequalities for Hadwiger's harmonic quermassintegrals

    Lutwak, E., Mar 1988, In : Mathematische Annalen. 280, 1, p. 165-175 11 p.

    Research output: Contribution to journalArticle

    Harmonic