Analytische Aspekt des optimalen Transports

• Antragsteller: Professor Dr. Michael Röckner
• Fachliche Zuordnung: Mathematik
• Förderung: Förderung von 2016 bis 2019
• Projektkennung: Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 316972354

• Erstellungsjahr: 2020

Zusammenfassung der Projektergebnisse

During the work on the project, its main goals have been achieved and the announced programme has been successfully fulfilled. Considerable progress has been achieved in the study of optimal transportation of measures and in the investigation of a large circle of related problems in the theory of Fokker–Planck–Kolmogorov equations, infinite dimensional analysis and measure theory. A fruitful cooperation between the groups involved in the project resulted in solving several important problems and opening new perspectives of research, which forms a basis of future cooperation and continuation of the collaboration.

Projektbezogene Publikationen (Auswahl)

• Estimates of distances between solutions of Fokker–Planck–Kolmogorov equations with partially degenerate diffusion matrices. Theory of Stochastic Processes. 2018. V. 23, N 2. P. 41–54
  O.A. Manita, M.S. Romanov, S.V. Shaposhnikov
  
• Poincaré and Brunn-Minkowski inequalities on the boundary of weighted Riemannian manifolds. American Journal of Mathematics. 2018. V. 140, N 5. P. 1147–1185
  A.V. Kolesnikov, E. Milman
  (Siehe online unter https://doi.org/10.1353/ajm.2018.0027)
• The KLS isoperimetric conjecture for generalized Orlicz balls. Annals of Probability. 2018. V. 46, N 6. P. 3578–3615
  A.V. Kolesnikov, E. Milman
  (Siehe online unter https://doi.org/10.1214/18-AOP1257)
• The Poisson equation and estimates for distances between stationary distributions of diffusions. Journal of Mathematical Sciences (New York). 2018. V. 232, N 3. P. 254–282
  V.I. Bogachev, M. Röckner, S.V. Shaposhnikov
  (Siehe online unter https://doi.org/10.1007/s10958-018-3872-3)
• Convergence in variation of solutions of nonlinear Fokker–Planck–Kolmogorov equations to stationary measures. Journal of Functional Analysis. 2019. V. 276, N 12. P. 3681–3713
  V.I. Bogachev, M. Röckner, S.V. Shaposhnikov
  (Siehe online unter https://doi.org/10.1016/j.jfa.2019.03.014)
• Extremal Kähler–Einstein metric for two-dimensional convex bodies. Journal of Geometric Analysis. 2019. V. 29, N 3. P. 2347–2373
  B. Klartag, A.V. Kolesnikov
  (Siehe online unter https://doi.org/10.1007/s12220-018-0077-4)
• On the Ambrosio–Figalli–Trevisan superposition principle for probability solutions to Fokker–Planck–Kolmogorov equations. Journal of Dynamics and Differential Equations. 2020
  V.I. Bogachev, M. Röckner, S.V. Shaposhnikov
  (Siehe online unter https://doi.org/10.1007/s10884-020-09828-5)
• Representations of solutions to Fokker–Planck–Kolmogorov equations with coefficients of low regularity. Journal of Evolution Equations. 2020. V. 20, N 2
  V.I. Bogachev, S.V. Shaposhnikov
  (Siehe online unter https://doi.org/10.1007/s00028-019-00532-6)
• On the Gardner–Zvavitch conjecture: symmetry in the inequalities of Brunn–Minkowski type. Advances in Mathematics. 2021
  A.V. Kolesnikov, G. Livshyts
  (Siehe online unter https://doi.org/10.1016/j.aim.2021.107689)
• Total variation distance estimates via L2-norm for polynomials in log-concave random vectors. International Mathematics Research Notices. 2021
  E.D. Kosov
  (Siehe online unter https://doi.org/10.1093/imrn/rnz278)