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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

    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

    A dual of the isepiphanic inequality

    Lutwak, E., Dec 1976, In : Archiv der Mathematik. 27, 1, p. 206-208 3 p.

    Research output: Contribution to journalArticle

    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

    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

    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

    A general isepiphanic inequality

    Lutwak, E., 1984, In : Proceedings of the American Mathematical Society. 90, 3, p. 415-421 7 p.

    Research output: Contribution to journalArticle

    Power Mean
    Convex Body
    Projection
    Geometric Inequalities
    Isoperimetric Inequality

    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

    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
    Affine Invariant
    Isoperimetric Inequality
    Polytopes
    Projection
    Reverse Inequality

    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

    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

    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

    A width-diameter inequality for convex bodies

    Lutwak, E., Apr 30 1983, In : Journal of Mathematical Analysis and Applications. 93, 1, p. 290-295 6 p.

    Research output: Contribution to journalArticle

    Convex Body
    Power Mean

    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

    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

    Characterization of the n-dimensional parallelotope

    Guggenheimer, H. & Lutwak, E., 1976, In : American Mathematical Monthly. 83, 6, p. 475-478

    Research output: Contribution to journalArticle

    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
    entropy
    Entropy
    Random variables

    Dual cross-sectional measures

    Lutwak, E., 1975, In : Atti Acccad Naz Lincei Rend Cl Sci Fis Mat Natur. 58, p. 1-5

    Research output: Contribution to journalArticle

    Dual mixed volumes

    Lutwak, E., 1975, In : Pacific Journal of Mathematics. 58, 2, p. 531-538

    Research output: Contribution to journalArticle

    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

    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

    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

    General Bieberbach inequality

    Lutwak, E., 1975, In : Mathematical Proceedings of the Cambridge Philosophical Society. 78, NOV, p. 493-495

    Research output: Contribution to journalArticle

    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

    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

    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

    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

    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

    Intersection bodies and dual mixed volumes

    Lutwak, E., 1988, In : Advances in Mathematics. 71, 2, p. 232-261 30 p.

    Research output: Contribution to journalArticle

    Intersection Body
    Mixed Volume

    INTRODUCTION

    Goodman, J. E., Lutwak, E., Malkevitch, J. & Pollack, R., 1985, In : Annals of the New York Academy of Sciences. 440, 1, p. ix-xii

    Research output: Contribution to journalEditorial

    Isoperimetric inequalities involving bisectors

    Lutwak, E., 1980, In : Bulletin of the London Mathematical Society. 12, p. 289-295

    Research output: Contribution to journalArticle

    Isoperimetric inequalities related to a problem of Moser

    Lutwak, E., 1979, In : American Mathematical Monthly. 86, 6, p. 476-477

    Research output: Contribution to journalArticle

    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

    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

    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

    Mean dual and harmonic cross-sectional measures

    Lutwak, E., Dec 1979, In : Annali di Matematica Pura ed Applicata, Series 4. 119, 1, p. 139-148 10 p.

    Research output: Contribution to journalArticle

    Harmonic
    Convex Body

    Mixed affine surface area

    Lutwak, E., Aug 1 1987, In : Journal of Mathematical Analysis and Applications. 125, 2, p. 351-360 10 p.

    Research output: Contribution to journalArticle

    Surface area

    Mixed projection inequalities

    Lutwak, E., 1985, In : Transactions of the American Mathematical Society. 287, 1, p. 91-106 16 p.

    Research output: Contribution to journalArticle

    Projection
    Geometry
    Convex Body
    Geometric Inequalities
    Affine geometry

    Mixed width-integrals of convex bodies

    Lutwak, E., Sep 1977, In : Israel Journal of Mathematics. 28, 3, p. 249-253 5 p.

    Research output: Contribution to journalArticle

    Convex Body
    Mixed Volume
    Isoperimetric Inequality
    Concurrent
    Cross section

    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

    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

    On a complementary Minkowski inequality

    Lutwak, E., 1979, In : Journal of Mathematical Analysis and Applications. 72, 1, p. 70-74 5 p.

    Research output: Contribution to journalArticle

    Brunn-Minkowski Inequality
    Minkowski's inequality

    On a conjectured projection inequality of Petty

    Lutwak, E., 1989, Integral geometry and tomography: Arcata CA. American Mathematical Society, p. 171-182 (Contemporary Mathematics; vol. 113).

    Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

    On cross-sectional measures of polar reciprocal convex bodies

    Lutwak, E., May 1976, In : Geometriae Dedicata. 5, 1, p. 79-80 2 p.

    Research output: Contribution to journalArticle

    Convex Body

    On packing curves into circles

    Lutwak, E., 1982, Convexity and related combinatorial geometry: Norman, Oklahoma 1980. 107111. (Lecture Notes in Pure and Applied Mathematics; vol. 76).

    Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)

    On power means of positive quadratic forms

    Lutwak, E., 1984, In : Linear Algebra and Its Applications. 57, C, p. 13-19 7 p.

    Research output: Contribution to journalArticle

    Power Mean
    Quadratic form
    Positive definite
    Thing
    Matrix Inequality

    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

    On some affine isoperimetric inequalities

    Lutwak, E., 1986, In : Journal of Differential Geometry. 23, 1, p. 1-13 13 p.

    Research output: Contribution to journalArticle

    Isoperimetric Inequality