Convex and Discrete Geometry


Valuations on Function Spaces
FWF Project (Award number P 25515)


Principal Investigator

Monika Ludwig

Project Duration

3/2013 - 2/2018

Researchers

Mohammad Ivaki (9/2013 - 8/2014)
Dan Ma (7/2014 - 12/2015)
Fabian Mussnig (3/2015 - 7/2017)
Michael Ober (10/2014 - 2/2015)
Laura Silverstein (9/2013 - 9/2016)
Tuo Wang (3/2013 - 3/2014)

Publications

  1. Fabian Mussnig:
    Valuations on log-concave functions
    JOURNAL OF GEOMETRIC ANALYSIS, in press.
  2. Andrea Colesanti, Monika Ludwig and Fabian Mussnig:
    Hessian valuations
    INDIANA UNIVERSITY MATHEMATICS JOURNAL 69, 1275-1315 (2020).
  3. Andrea Colesanti, Monika Ludwig and Fabian Mussnig:
    Valuations on convex functions
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES NOTICES 2019, No. 8, 2384-2410 (2019).
  4. Minkowski valuations on lattice polytopes
    JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY (JEMS) 21, 163-197 (2019).
    Jointly with Károly J. Böröczky.
  5. Weighted floating bodies and polytopal approximation
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 370, 7129-7148 (2018).
    Jointly with Florian Besau and Elisabeth Werner.
  6. Károly J. Böröczky and Monika Ludwig:
    Valuations on lattice polytopes
    In: Tensor Valuations and their Applications in Stochastic Geometry and Imaging
    (M. Kiderlen and E. Vedel Jensen, eds.), Springer Lecture Notes in Mathematics 2177, 213-234 (2017).
  7. Andrea Colesanti, Monika Ludwig and Fabian Mussnig:
    Minkowski valuations on convex functions
    CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS 56, Art. 162 (2017).
  8. Jin Li and Dan Ma:
    Laplace transforms and valuations
    JOURNAL OF FUNCTIONAL ANALYSIS 272, 738-758 (2017).
  9. Monika Ludwig and Matthias Reitzner:
    SL(n) invariant valuations on polytopes
    DISCRETE AND COMPUTATIONAL GEOMETRY 57, 571-581 (2017).
  10. Monika Ludwig and Laura Silverstein:
    Tensor valuations on lattice polytopes
    ADVANCES IN MATHEMATICS 319, 76-110 (2017).
  11. Mohammad N. Ivaki:
    A note on the Gauss curvature flow.
    INDIANA UNIVERSITY MATHEMATICS JOURNAL 65, 743-751 (2016).
  12. Mohammad N. Ivaki:
    The planar Busemann-Petty centroid inequality and its stability.
    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 368, 3539-3563 (2016).
  13. Michael Ober:
    Asymmetric Lp convexification and the convex Lorentz-Sobolev inequality.
    MONATSHEFTE FÜR MATHEMATIK 179, 113-127 (2016).
  14. Tuo Wang:
    On the discrete Lp Minkowski problem
    INTERNATIONAL MATHEMATICS RESEARCH NOTICES 2015, no. 20, 10563-10585 (2015).
  15. Monika Ludwig:
    Anisotropic fractional Sobolev norms
    ADVANCES IN MATHEMATICS 252, 150 - 157 (2014).
  16. Tuo Wang:
    Semivaluations on BV(Rn)
    INDIANA UNIVERSITY MATHEMATICS JOURNAL 63, 1447-1465 (2014).
  17. Tuo Wang:
    The affine Pólya-Szegö principle: Equality cases and stability
    JOURNAL OF FUNCTIONAL ANALYSIS 265, 1728-1748 (2013).