Joint with Mario Santilli,
"Regularity of distance functions from arbitrary closed sets",
preprint.
Mathematische Annalen, 2022.
Joint with Antonio De Rosa and Mario Santilli,
"Uniqueness of critical points of the anisotropic isoperimetric problem for finite perimeter sets",
Arch. Ration. Mech. Anal., 238, no. 3, 1157--1198, 2020,
readcube,
preprint.
Corrigendum
Joint with Antonio De Rosa,
"Equivalence of the ellipticity conditions for geometric variational problems",
Comm. Pure Appl. Math., 73, no. 11, 2473--2515, 2020,
preprint.
Joint with 方扬钦 (Yangqin Fang),
"Existence of solutions to a general geometric elliptic variational problem",
Calc. Var. PDE, Vol. 57(3), 2018 ,
preview,
preprint.
"Estimating discrete curvatures in terms of beta numbers", preprint.
"Higher order rectifiability of measures via averaged discrete curvatures", Rev. Mat. Iberoamericana, Vol. 33, 861-884, 2017, preprint.
Joint with Paweł Strzelecki and Heiko von der Mosel,
"Compactness and isotopy finiteness for submanifolds
with uniformly bounded geometric curvature energies",
preprint.
Comm. Anal. Geom., Vol. 26, No. 6 (2018), pp. 1251-1316.
Joint with Ulrich Menne,
"Decay rates for the quadratic and super-quadratic tilt-excess of integral varifolds",
Nonlinear Differ. Equ. Appl. (NoDEA), Vol. 24(2), 2017,
preview,
preprint.
"Geometric Sobolev-like embedding using high-dimensional Menger-like curvature", Trans. Amer. Math. Soc., Vol. 367, 775-811, 2015, preprint.
Joint with Paweł Strzelecki and Heiko von der Mosel,
"Characterizing $W^{2,p}$ submanifolds by $p$-integrability of global curvatures",
Geom. Funct. Anal., Vol. 23(3), 937–984, 2013,
preprint.
Joint with Simon Blatt,
"Sharp Boundedness and Regularizing effects of the integral Menger curvature for submanifolds",
Adv. Math., Vol. 230(3), 839–852, 2012,
preprint.
Joint with Marta Szumańska,
"Minimal Hölder regularity implying finiteness of integral Menger curvature",
Manuscripta Math., Vol. 141, Issue 1, 125–147, 2013,
preprint.
Ph.D. Thesis,
"Integral Menger curvature for sets of arbitrary dimension and codimension",
a differently typesetted
version is available also at
arXiv:1011.2008.
Ramark: The article
"Geometric Sobolev-like embedding using high-dimensional Menger-like curvature"
obsoletes my thesis. For any further reference one should use
the published version.
"Regularity of weak solutions of $n$-dimensional H-systems", Differential and Integral Equations, Vol. 23, Num. 11-12, 1073-1090, 2010.
"The Plateau problem – old and new",
Geometric analysis and related topics,
Będlewo, 17-21 June, 2017;
Harmonic Analysis and Geometric Measure Theory,
Marseille, October 2 - 6, 2017.
"Geometric curvature energies in calculus of variations",
New Trends in Calculus of Variations and Partial Differential Equations
Napoli, 21-23 November, 2013
"Menger curvature for set of arbitrary dimension",
CODY Final Meeting:
Renormalization in low dimensional dynamics and its applications,
Warwick, 12-18 December, 2010.
"Ellipticity in geometric variational problems",
Colloquium of MIM,
Warsaw, 08 December 2022.
"Eliptyczność w geometrycznych zagadnieniach wariacyjnych",
Open seminar on PDEs,
Warsaw, 25 November 2021.
"Geometric Ellipticity",
NCTS Differential Geometry Seminar,
Taipei, 21 October 2021, video.
"Regularność anizotropowej odległości od zbioru",
Seminarium – Analiza Nieliniowa,
Łódź, 19 October 2021.
"Geometric Ellipticity",
Geometric Measure Theory and applications,
Cortona, 31 August 2021, video.
"The Alexandrov Theorem in Minkowski Spaces",
Monaday's Nonstandard Seminar,
Warsaw, 29 March 2021.
"New and old solutions to generalised Plateau’s problems",
X Forum of partial differential equations,
Będlewo, 19 – 24 June 2016.
"New and old solutions to a generalised Plateau’s problem",
Oberseminar ANALYSIS - PROBABILITY,
Leipzig, 14 June 2016.
"Some aspects of regularity theory for
integral varifolds",
6. Forum Matematyków Polskich,
Warsaw, 7 - 12 September 2015.
"Całkowa krzywizna Mengera dla
zbiorów dowolnego wymiaru i kowymiaru" (polish),
Ph.D. defence, Warsaw, 08 May, 2012.
"Higher dimensional Menger
curvature as a tool for proving regularity of sets",
2nd EU Young and Mobile Workshop: Geometric Analysis and PDE's,
Granada, 30 November, 2011.
"Integral Menger curvature for
sets of arbitrary dimension and codimension",
Seminar of Mathematical Physics Equations Group,
Warsaw, 31 March, 2011.
Workshop in Geometry and Analysis
07 – 18 October 2019, Warsaw, Poland
Lecture notes [updated on: 25 October 2019]
Seminar
Geometric function and mapping theory.
22 November 2018, Warsaw, Poland
Talk titled:
Equivalence of ellipticity conditions for geometric variational problems.
Seminar
Topologia algebraiczna
23 October 2018, Warsaw, Poland
Talk titled:
Ellipticity in geometric variational problems.
A Seminar on Geometric Measure Theory, Varifolds, and Their Applications
9 – 12 July 2018, Portland, OR, USA
Seminar
Geometric function and mapping theory.
24 May 2018, Warsaw, Poland
Talk titled:
Ellipticity in geometric variational problems.
Mini-course on the Allard Regularity Theorem
16 – 20 April 2018, Warsaw, Poland
CIMI Analysis Semester.
Week I:
Geometric measure theory: analysis and non-smooth objects.
12 – 16 September 2016, Toulouse, France
Handout ---
Lecture notes
e-mail: initial.lastname @ mimuw.edu.pl |