[stepanov]

Full Professor, St. Petersburg Branch of the Steklov Research Institute of Mathematics of the Russian Academy of Sciences

**Email:** *stepanov.eugene AT gmail.com*

- T. Guo - N. Karagodin - E. Stepanov (Preprint)

Optimal functional product quantization (2023) - E. Paolini - E. Stepanov (Preprint)

On the Steiner tree connecting a fractal set (2023) - M. Novaga - E. Paolini - E. Stepanov - V. M. Tortorelli (
*Networks and Heterogeneous Media*)

Isoperimetric planar clusters with infinitely many regions (2023) - G. Alberti - A. Massaccesi - E. Stepanov (
*J. Diff. Geom.*)

On the geometric structure of currents tangent to smooth distributions (2022) - M. Novaga - E. Paolini - E. Stepanov - V. M. Tortorelli (
*J. Geom. Anal.*)

Isoperimetric clusters in homogeneous spaces via concentration compactness (2022) - E. Stepanov - D. Trevisan (
*J. Differential Equations*)

On exterior differential systems involving differentials of H\"{o}lder functions (2022) - A. Kroshnin - E. Stepanov - D. Trevisan (
*ESAIM: COCV*)

Infinite multidimensional scaling for metric measure spaces (2022) - S. Kryzhevich - E. Stepanov (Accepted Paper:
*Springer Proceedings dedicated to DCO 2021*)

Constructive controllability for incompressible vector fields (2021) - C. Rigoni - E. Stepanov - D. Trevisan (
*J. London Math. Soc.*)

Lie brackets of nonsmooth vector fields and commutation of their flows (2020) - E. Stepanov - D. Trevisan (
*J. Geom. Anal.*)

Towards geometric integration of rough differential forms (2020) - N. Puchkin - V. Spokoiny - E. Stepanov - D. Trevisan (Preprint)

Reconstruction of manifold embeddings into Euclidean spaces via intrinsic distances (2020) - S. Kryzhevich - E. Stepanov (
*J. Differential Equations*)

The saga of a fish: from a survival guide to closing lemmas (2019) - G. Alberti - E. Stepanov - D. Trevisan (Preprint)

Integration of nonsmooth $\boldsymbol{2}$-forms: from Young to Itô and Stratonovich (2019) - E. Paolini - E. Stepanov (
*Proc. Royal Soc. Edinburgh Ser. A - Mathematics*)

Flows of measures generated by vector fields (2018) - V. Magnani - E. Stepanov - D. Trevisan (
*J. Lond. Math. Soc.*)

A rough calculus approach to level sets in the Heisenberg group (2018) - A. Ponosov - E. Stepanov (
*SIAM J. Control and Optimization*)

Smooth dynamics becomes hybrid in the limit (2017) - E. Stepanov - D. Trevisan (
*J. Funct. Anal.*)

Three superposition principles: currents, continuity equations and curves of measures (2017) - A. Chambolle - J. Lamboley - A. Lemenant - E. Stepanov (
*SIAM J. Math. Anal.*)

Regularity for the optimal compliance problem with length penalization (2017) - E. Stepanov - Y. Teplitskaya (
*J. London Math. Soc.*)

Self-contracted curves have finite length (2017) - E. Paolini - E. Stepanov - Y. Teplitskaya (
*Adv. Calc. Var.*)

An example of an infinite Steiner tree connecting an uncountable set (2015) - A. Ponosov - E. Stepanov (
*St. Petersburg Math. J*)

Atomic operators, random dynamical systems and invariant measures (2014) - V. Georgiev - E. Stepanov (
*Discrete Contin. Dyn. Syst.*)

Metric cycles, curves and solenoids (2014) - M. Novaga - A. Sobolevski - E. Stepanov (
*Pacific J. Math.*)

Droplet condensation and isoperimetric towers (2013) - G. Buttazzo - F. Santambrogio - E. Stepanov (
*Ann. Scuola Norm. Sup. Pisa Cl. Sci.*)

Asymptotic optimal location of facilities in a competition between population and industries (2013) - E. Paolini - E. Stepanov (
*J. Funct. Anal.*)

Structure of metric cycles and normal one-dimensional currents (2013) - E. Paolini - E. Stepanov (
*J. Funct. Anal.*)

Decomposition of acyclic normal currents in a metric space (2012) - E. Paolini - E. Stepanov (
*Calc. Var. Partial Diff. Equations*)

Existence and regularity results for the Steiner problem (2012) - E. Stepanov (
*J. Math. Sciences (N.Y.)*)

Rectifiability of metric flat chains and fractional masses (2010) - G. Buttazzo - E. Mainini - E. Stepanov (
*Control Cybernet.*)

Stationary configurations for the average distance functional and related problems (2009) - E. Paolini - E. Stepanov (
*J. Math. Sciences (N.Y.)*)

Connecting measures by means of branched transportation networks at finite cost (2009) - G. Buttazzo - A. Pratelli - S. Solimini - E. Stepanov (
*Springer Lecture Notes in Mathematics*)

Optimal urban networks via mass transportation (2009) - A. Brancolini - G. Buttazzo - F. Santambrogio - E. Stepanov (
*ESAIM Control Optim. Calc. Var.*)

Long-term planning versus short-term planning in the asymptotical location problem (2009) - G. Buttazzo - A. Pratelli - E. Stepanov (
*SIAM J. Opt*)

Optimal pricing policies for public transportation networks (2006) - E. Stepanov (
*J. Math. Sci. (N.Y.)*)

Partial geometric regularity of some optimal connected transportation networks (2006) - M. Drakhlin - E. Litsyn - A. Ponosov - E. Stepanov (
*J. Nonlinear & Convex Anal.*)

Generalizing the property of locality: atomic/coatomic operators and applications (2006) - M. Miranda Jr - E. Paolini - E. Stepanov (
*Calc. Var. Partial Diff. Equations*)

On one-dimensional continua uniformly approximating planar sets (2006) - E. Paolini - E. Stepanov (
*Interfaces and Free Boundaries*)

Optimal transportation networks as flat chains (2006) - G. Buttazzo - E. Stepanov (
*Discrete Contin. Dyn. Syst.*)

Transport density in Monge-Kantorovich problems with Dirichlet conditions (2005) - G. Buttazzo - E. Stepanov (
*Calculus of Variations: Topics from the Mathematical Heritage of Ennio De Giorgi, D. Pallara (ed.), Quaderni di Matematica, Seconda Universit\`{a} di Napoli, Caserta*)

Minimization problems for average distance functionals (2004) - E. Paolini - E. Stepanov (
*J. Math. Sciences (N.Y.)*)

Qualitative properties of maximum distance minimizers and average distance minimizers in $\mathbf R^n$ (2004) - A. Ponosov - E. Stepanov (
*International conference on fixed point theory and its applications (Valencia, 2003), G.G. Falset, E.L Fuster, B. Sims (ed.), Yokohama publishers, Yokohama*)

Invariant measures for generalized random dynamical systems (2004) - E. Stepanov (
*Proc. Edunburgh Math. Soc.*)

Representation of atomic operators and extension problems (2004) - G. Buttazzo - E. Stepanov (
*Ann. Sc. Norm. Sup. Pisa Cl. Sci.*)

Optimal transportation networks as free Dirichlet regions for the Monge-Kantorovich problem (2003) - G. Buttazzo - E. Stepanov (
*SIAM J. Control Optim.*)

On regularity of transport density in the Monge-Kantorovich problem (2003) - E. Stepanov (
*J. Nonlinear and Convex Anal.*)

Relaxation of optimal control problems with shifted controls (2002) - G. Buttazzo - E. Oudet - E. Stepanov (
*Progress in Nonlinear Diff. Equations and their Applications*)

Optimal transportation problems with free Dirichlet regions (2002) - E. Stepanov (
*Proc. Amer. Math. Soc.*)

Relaxation and convexity of functionals with pointwise nonlocality (2002) - E. Stepanov - P. Tilli (
*Proc. Royal Soc. Edinburgh - Ser. A. (Mathematics)*)

On the Dirichlet problem with several volume constraints on the level sets (2002) - M. Drakhlin - A. Ponosov - E. Stepanov (
*Proc. Edinburgh Math. Soc.*)

On some classes of operators determined by the structure of their memory (2002) - E. Stepanov - A. Zdorovtsev (
*J. Convex Anal.*)

Relaxation of some nonlocal integral functionals in weak topology of Lebesgue spaces (2001) - L. De Pascale - E. Stepanov (
*Trans. Amer. Math. Soc.*)

Weak and strong density of compositions (2000)

*22 apr 2020:*Nonwandering points of continuous dynamical systems and constructive controllability*25 oct 2017:*The saga of a fish: from a survival guide to closing lemmas for dynamical systems*10 dec 2014:*Properties of the free boundary in the optimal compliance problem*23 oct 2013:*Flows generated by measurable vector fields*12 dec 2012:*Vector fields, currents and rectifiable curves in metric spaces*7 dec 2011:*Schwartzman's solenoids and Ambrosio-Kirchheim currents*1 dec 2010:*One-dimensional currents and curves*3 dec 2008:*Regularity for the "antique" Steiner problem*28 nov 2007:*Transportation of measures through branched networks at finite cost*15 feb 2001:*Local operators and the problem of J. von Neumann on $\sigma$-homomorphisms

*6 sep 2022 - 7 sep 2022:*Optimal Transport and Uncertanity - second edition*26 nov 2021 - 26 nov 2021:*Optimal transport and uncertanity*30 aug 2021 - 3 sep 2021:*Geometric Measure Theory and applications*27 oct 2014 - 31 oct 2014:*ERC Workshop on Optimal Transportation and Applications

*20 jun 2022 - 24 jun 2022:*Isoperimetric Problems*14 sep 2020 - 17 sep 2020:*Geometric Measure Theory and Geometric Analysis in Moscow*23 sep 2019 - 27 sep 2019:*Workshop "Recent advances in mass transportation"*14 may 2018 - 18 may 2018:*Mini-colloquium «Rough differential calculus and weak geometric structures»