Thierry De Pauw

MATHEMATICIAN

Das Wesen der Mathematik liegt in ihrer Freiheit.

Georg Cantor

L’homme ne peut s’empêcher d’être le personnage principal.

Eric Chevillard

La vie est une tragédie quand on la regarde de près. Mais avec un peu de recul, c’est une comédie.

Francis Dannemark

Always remember, the person we’re really working for is the person who’s restoring the piece a hundred years from now.

Donna Tartt

PUBLICATIONS

  • Abstract charges (With Ph. Bouafia). In preparation.
  • Another simple proof of the 1-dimensional flat chain conjecture (With Ph. Bouafia). Submitted. arxiv.
  • Divergence operators: Free space and vanishing charges. Submitted. arxiv.
  • Localized locally convex topologies. Submitted. arxiv.
  • A brief review of Radon-Nikodýmification. arxiv.
  • Quantified compactness in Lipschitz-free spaces of [-1,1]n. To appear in Trans. Amer. Math. Soc. arxiv.
  • Banach-Lamperti theorem for the Kurzweil-Henstock integral. Ann. Fenn. Math., 51, 2026, 223-236. journal. arxiv.
  • A regularity property of fractional Brownian sheets (With Ph. Bouafia). J. Fractal Geom., 12, 2025, 265-302. journal. arxiv.
  • A representation formula for members of SBV dual (With Ph. Bouafia). Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), 25(1), 2024, 483-493. journal. arxiv.
  • Undecidably semolicalizable metric measure spaces. Commun. Contemp. Math., 26(4), 2024 journal.
  • Radon-Nikodýmification of arbitrary measure spaces (With Ph. Bouafia). Extracta Math., 38(2), 2023, 193-203. journal.
  • On the existence of mass minimising G chains in finite dimensional normed spaces (With I. Vasilyev). Ann. Inst. Fourier, 73(2), 2023, 635-694. journal.
  • Density estimate from below in relation to a conjecture of A. Zygmund on Lipschitz differentiation. J. Ec. polytech. Math., 9, 2022, 1473-1512. journal.
  • Linear isoperimetric inequality for normal and integral currents in compact subanalytic sets (With R. Hardt). J. Singul., 24, 2022, 145-168. journal.
  • Comments on Washek Pfeffer’s contributions to integration theory. Obituary. Real Anal. Exchange, 46(2), 2021, 1-9. project euclid.
  • Partial regularity of almost minimising rectifiable G chains in Hilbert space (With R. Züst). Amer. J. Math., 141(6), 2019, 1591-1705. jstor. arxiv.
  • Homology of normal chains and cohomology of charges (With R. Hardt and W.F. Pfeffer). Memoirs Amer. Math. Soc. 247 n° 1172, 2017, v+115pp. journal.
  • An example pertaining to the failure of the Besicovitch-Federer structure Theorem in Hilbert space. Publ. Mat., 61(1), 2017, 153-173. jstor.
  • On sets minimising their weighted length in uniformly convex separable Banach spaces (With A. Lemenant and V. Millot). Adv. Math., 305, 2017, 1268-1319. journal.
  • Multiple valued maps into separable Hilbert space that almost minimise their p energy or are squeeze and squash stationary (With Ph. Bouafia and C.Y. Wang). Calc. Var. Partial Diff. Eq., 54(2), 2015, 2167-2196. journal. arxiv.
  • Existence of p harmonic multiple valued maps into separable Hilbert space (With J. Goblet and Ph. Bouafia). Ann. Inst. Fourier, 65(2), 2015, 763-833. journal.
  • Integral geometric measure in separable Banach space (with Ph. Bouafia). Math. Ann., 363(1-2), 2015, 269-304. journal.
  • Approximation by polyhedral G chains in Banach spaces. Z. Anal. Anwend., 33, 2014, 311-334. journal.
  • Some basic Theorems on flat G chains (With R. Hardt). J. Math. Anal. Appl., 418, 2014, 1046-1061. journal.
  • Rectifiable and flat G chains in metric spaces (With R. Hardt). Amer. J. Math., 134(1), 2012, 1-69. jstor. muse.
  • On the distributional divergence of vector fields vanishing at infinity (With M. Torres). Proc. Roy. Soc. Edinburgh Sect. A, 141(1), 2011, 65-76. journal.
  • Size minimizing surfaces. Ann. Sci. Ecole Norm. Sup., 42(1), 2009, 37-101. numdam.
  • Charges in middle dimensions (With L. Moonens and W.F. Pfeffer). J. Math. Pures Appl., 92(1), 2009, 86-112. journal.
  • Linearly approximatable functions (With A. Koeller). Proc. Amer. Math. Soc., 137, 2009, 1347-1356. journal.
  • A generalization of Reifenberg’s theorem in ℝ3 (With G. David and T. Toro). Geom. Funct. Anal., 18, 2008, 1168-1235. journal.
  • Distributions for which div v = F has a continuous solution (With W.F. Pfeffer). Commun. Pure Appl. Math., 61(2), 2008, 230-260. journal.
  • The divergence Theorem for unbounded vector fields (With W.F. Pfeffer). Trans. Amer. Math. Soc., 359(12), 2007, 5915-5929. journal.
  • Concentrated, nearly monotonic, epiperimetric measures in Euclidean space. J. Differential Geom., 77(1), 2007, 77-134. project euclid.
  • Comparing homologies : Cech’s theory, singular chains, integral flat chains and integral currents. Rev. Mat. Iberoamericana, 23(1), 2007, 143-189. project euclid.
  • Autour du théorème de la divergence. Panor. Synthèses, 18, 2004, 85-121. journal.
  • Applications of scans and fractional power integrands (With R. Hardt). Progr. Nonlinear Partial Differential Equations Appl., 59, 2004, 19-31. journal.
  • The Gauss-Green Theorem and removable sets for 2nd order PDEs in divergence form (With W.F. Pfeffer). Adv. Math., 183(1), 2004, 155-182. journal.
  • On the exceptional set of the flux of a bounded vector field. J. Math. Pures Appl.,82(9), 2003, 1191-1217. journal.
  • Size minimization and approximating problems (With R. Hardt). Calc. Var. Partial Diff. Eq., 17(4), 2003, 405-442. journal.
  • Points of ɛ differentiability of Lipschitz functions from ℝn to ℝn-1. (With P. Huovinen). Bull. London Math. Soc., 34, 2002, 539-550. journal.
  • Nearly flat almost monotone measures are big pieces of Lipschitz graphs. J. Geom. Anal., 12(1), 2002, 29-61. journal.
  • Charges, BV functions and multipliers for generalized Riemann integrals (With Z. Buczolich and W.F. Pfeffer). Indiana Univ. Math. J., 48(4), 1999, 1471-1511. jstor.
  • Multipliers for generalized Riemann integrals (With Z. Buczolish and W.F. Pfeffer). C.R. Math. Acad. Sci. Soc. R. Can., 21(4), 1999, 139-145. journal.
  • On explicit solutions for the problem of Mumford and Shah (With D. Smets). Commun. Contemp. Math., 1(2), 1999, 201-212. journal.
  • Multipliers for one-dimensional non-absolutely convergent integrals. Atti Sem. Mat. Fis. Univ. Modena, XLVII, 1999, 35-43.
  • On SBV Dual. Indiana Univ. Math. J., 47(1), 1998, 99-121. jstor.
  • Topologies for the space of BV-integrable functions in ℝn. J. Funct. Anal., 144(1), 1997, 190-232. journal.
  • A concept of generalized absolute continuity for the F-integral. Real Anal. Exch., 22(1), 1996-97, 350-361. project euclid.