List of publications

• Rataj J., Winter S.: On volume and surface area of parallel sets. II. Surface measures and (non-)differentiability of the volume. arXiv 2301.07429. Submitted.

Research papers:

• Rataj J., Winter S., Zähle M.: Mean Lipschitz-Killing curvatures for homogeneous random fractals. arXiv 2107.14431. J. Fractal Geom. 10 (2023), 1-42.
• Rataj J.: Mean Euler characteristic of stationary random closed sets. <\i> Stoch. Proc. Appl. 137 (2021), 252-271.
• Rataj J., Zajíček L.: Smallness of the set of critical values of distance functions in two-dimensional Euclidean and Riemannian spaces. arXiv 1903.09492. Mathematika 66 (2020), 297-324.
• Pokorný D., Rataj J., Zajíček L.: On the structure of WDC sets. arXiv 1703.09520. Math. Nachr. 292 (2019), 1595-1626.
• Kiderlen M., Rataj J.: Dilation volumes of sets of bounded perimeter. arXiv 1708.09191. Adv. in Appl. Probab. 50 (2018), 1095–1118, DOI 10.1017/apr.2018.52.
• Hug D., Rataj J.: Mixed curvature measures of translative integral geometry. arXiv 1606.04224. Geom. Dedicata 195 (2018), 101–120, DOI 10.1007/s10711-017-0278-1.
• Hug D., Rataj J., Weil W.: Flag representations of mixed volumes and mixed functionals of convex bodies. arXiv 1705.04816. J. Math. Anal. Appl. 460 (2018), 745–776, DOI 10.1016/j.jmaa.2017.12.039.
• Rataj J., Zajíček L.: On the structure of sets with positive reach. arXiv 1604.08841. Math. Nachr. 290 (2017), 1806-1829, DOI 10.1002/mana.201600237.
• Goodey P., Hinderer W., Hug D., Rataj J., Weil W.: A flag representation of projection functions. arXiv 1502.06747 Adv. Geom. 17 (2017), 303-322, DOI 10.1515/advgeom-2017-0022
• Fu J.H.G., Pokorný D., Rataj J.: Kinematic formulas for sets defined by differences of convex functions. arXiv 1505.03388. Adv. Math. 311 (2017), 796-832
• Rataj J., Zähle M.: Legendrian cycles and curvatures. arXiv 1402.2249 J. Geom. Anal. 25 (2015), 2133-2147, DOI 10.1007/s12220-014-9506-1
• Rataj J.: Random sets of finite perimeter. arXiv 1401.1634 Math. Nachr. 288 (2015), 1047–1056, DOI 10.1002/mana.201300341
• Hug D., Rataj J., Weil W.: A product integral representation of mixed volumes of two convex bodies. arXiv 1112.0955. Adv. Geom. 13 (2013), 633–662
• Pokorný D., Rataj J.: Normal cycles and curvature measures of sets with d.c. boundary, arXiv 1209.2305. Adv. Math. 248 (2013), 963-985
• Rataj J., Zähle M.: Curvature densities of self-similar sets, arXiv 1009.6162. Indiana Univ. Math. J. 61 (2012) 4, 1425-1449
• Rataj J., Winter S.: Characterization of Minkowski measurability in terms of surface area, arXiv 1111.1825. J. Math. Anal. Appl. 400 (2013), 120-132
• Rataj J., Zajíček L.: Critical values and level sets of distance functions in Riemannian, Alexandrov and Minkowski spaces, Houston J. Math. 38 (2012) 2, 445-467
• Honzl O., Rataj J.: Almost sure asymptotic behaviour of the $r$-neighbourhood surface area of Brownian paths. Czechoslovak Math. J. 62 (2012) 1, 67-75
• Auneau J., Rataj J., Jensen E.B.V.: Closed form of the rotational Crofton formula. Math. Nachr. 285 (2012) 2-3, 164-180
• Rataj J., Winter S.: On volume and surface area of parallel sets, arXiv 0905.3279. Indiana Univ. Math. J. 59 (2010) 5, 1661-1686
• Rataj J., Zajíček L.: Properties of distance functions on convex surfaces and Alexandrov spaces, arXiv 0902.4020. Czechoslovak Math. J. 61 (2011), 247–269
• Mrkvička T., Rataj J.: On estimation of intrinsic volume densities of stationary random closed sets via parallel sets in the plane. Kybernetika 45 (2009), 931-945
• Rataj J., Spodarev E., Meschenmoser D.: Approximations of the Wiener sausage and its curvature measures. Ann. Appl. Probab. 19 (2009), 1840-1859
• Rataj J., Schmidt V., Spodarev E.: On the expected surface area of the Wiener sausage. Math. Nachr. 282 (2009) 4, 591-603
• Vedel Jensen E.B., Rataj J.: A rotational formula for intrinsic volumes. Adv. Appl. Math. 41 (2008), 530-560
• Rataj J.: Convergence of total variation of curvature measures. Monatsh. Math. 153 (2008), 153–164
• Mrkvička T., Rataj J.: On estimation of intrinsic volume densities of stationary random closed sets. Stoch. Proc. Appl. 118 (2008) 2, 213-231
• Kiderlen M., Rataj J.: On infinitesimal increase of volumes of morphological transforms. Mathematika 53 (2006), 103-127
• Rataj J.: Estimation of intrinsic volumes from parallel neighbourhoods. Suppl. Rend. Circ. Mat. Palermo, Ser. II, 77 (2006), 553-563
• Rataj J.: On boundaries of unions of sets with positive reach. Beiträge zur Algebra und Geometrie 46 (2005), 397-404
• Rataj J., Zähle M.: General normal cycles and Lipschitz manifolds of bounded curvature. Ann. Global Anal. Geom. 27 (2005), 135-156
• Rataj J.: On estimation of the Euler number by projections of thin slabs. Adv. in Appl. Probab. 36 (2004), b715-724
• Rataj J.: Absolute curvature measures for unions of sets with positive reach. Mathematika 49 (2002), 33-44
• Rataj J.: On set covariance and three-point test sets. Czechoslovak Math. J. 54 (2004), 205-214
• Rataj J., Zahle M.: Normal cycles of Lipschitz manifolds by approximation with parallel sets. Diff. Geom. Appl. 19 (2003), 113-126
• Rataj J., Zähle M.: A remark on mixed curvature measures for sets with positive reach. Beiträge zur Algebra und Geometrie 43 (2002), 171-179
• Rataj J.: Determination of spherical area measures by means of dilation volumes. Math. Nachr. 235 (2002), 143-162
• Rataj J., Zähle M.: Curvatures and Currents for Unions of Sets with Positive Reach, II. Ann. Global Anal. Geom. 20 (2001), 1-21
• Rataj J.: A translative integral formula for absolute curvature measures. Geom. Dedicata 84 (2001), 245-252
• Beneš V., Rataj J., Krejčíř P., Ohser J.: Projection measures and estimation variances of intensities. Statistics 32 (1999) 4, 369-393
• Rataj J.: Translative and kinematic formulae for curvature measures of flat sections. Math. Nachr. 197 (1999), 89-101
• Rataj J.: The iterated version of a translative integral formula for sets of positive reach. Rend. Circ. Mat. Palermo Ser. II, Suppl. 46 (1997), 129-138
• Rataj J., Saxl I.: Boolean cluster models: Mean cluster dilations and spherical contact distances. Math. Bohemica 122 (1997), 21-36
• Saxl I., Rataj J.: Spherical contact and nearest neighbour distances in Boolean cluster fields. Acta Stereol. 15 (1996), 91-96
• Rataj J.: Remarks to a translative formula for sets of positive reach. Geom. Dedicata 65 (1997), 59-62
• Rataj J.: Estimation of oriented normal direction distribution via mixed areas. Acta Stereol. 15 (1996), 77-82
• Rataj J.: Estimation of oriented direction distribution of a planar body. Adv. Appl. Probab. 28 (1996), 394-404
• Rataj J., Zähle M.: Mixed curvature measures for sets of positive reach and a translative integral formula. Geom. Dedicata 57 (1995), 259-283
• Rataj J.: Characterization of compact sets by their dilation volume. Math. Nachr. 173 (1995), 287-295
• Rataj J., Saxl I., Pelikán K.: Convergence of oscillating point patterns to the Poisson point process. Applications of Mathematics 38 (1993), 221-235
• Rataj J.: Random distances and edge correction. Statistics 24 (1993), 377-385
• Rataj J.: An intersection formula for Hausdorff rectifiable sets using mixed volumes of associated zonoids. Geometriae Dedicata 43 (1992), 65-69
• Rataj J., Saxl I.: Estimation of direction distribution of a planar fibre system. Acta Stereol. 11 Suppl.I (1992), 631-636
• Lešanovský A., Rataj J., Hojek S.: 0-1 sequences having the same numbers of (1-1) couples of given distances Math. Bohemica 117(1992), 271-282
• Lešanovský A., Rataj J.: Solution to Problem 89-5. IMS Bulletin 20 (1991), 564
• Saxl I., Rataj J.: Sférická kontaktní vzdálenost - charakteristika prostorového rozmístění částic (Spherical contact distance - characterization of spatial arrangement of particles). Pokroky práškové metalurgie 1-2 (1990), 88-160
• Rataj J., Pelikán K.: Korekce okrajových jevů při odhadu charakteristik geometrických struktur (Edge effect correction in estimation of characteristics of geometrical structures). Pokroky práškové metalurgie 1-2 (1990), 75-87
• Rataj J.: A characterization of weak convergence. Časopis pěst. mat. 115 (1990), 48-60
• Kroupa F., Nejezchleb K., Rataj J., Saxl I.: Non-homogeneous distribution of internal stresses and cracks in poled PZT ceramics. Ferroelectrics 100 (1989), 281-290
• Rataj J., Saxl I.: Analysis of planar anisotropy by means of the Steiner compact set. J. Appl. Probab. 26 (1989), 490-502
• Saxl I., Rataj J.: Random paths and interparticle distances. Acta Stereol. 7 (1988), 101-106
• Rataj J., Saxl I.: Analysis of planar anisotropy by means of the Steiner compact set: a simple graphical method. Acta Stereol. 7 (1988), 107-112
• Rataj J., Zítek F.: Sur la norme de Fourier, III. Časopis pěst. mat. 112 (1987), 312-319
• Rataj J.: Some remarks on Fourier seminorms. Časopis pěst. mat. 112 (1987), 368-372
• Preiss D., Rataj J.: Maximal sets of orthogonal measures are not analytic. Proc. Amer. Math. Soc. 93 (1985), 471-476

Monographs:

• Rataj J., Zähle M.: Curvature Measures of Singular Sets. Springer, Cham, 2019.
• Beneš V., Rataj J.: Stochastic Geometry: Selected Topics. Kluwer Academic Publishers, Boston 2004
  
• Saxl I., Pelikán K., Rataj J., Besterci M.: Quantification and Modelling of Heterogeneous Systems. Cambridge Interscience Publishing, Cambridge 1995

Text book:

Rataj J: Bodové procesy [Point Processes]. Karolinum, Praha 2000, second corrected edition 2006

Published conference contributions:

• Saxl I., Rataj J.: Random paths in non-convex bodies. In: Geobild '89 (A.Hübler, W.Nagel, B.D.Ripley & G.Werner eds.), Akademie-Verlag, Berlin (1989), 93-98
• Rataj J., Saxl I., Nejezchleb K., Kroupa F.: Nehomogenita povrchových jevů (Non-homogeneity of superficial efects. In: Fraktografia '89, Dom techniky ČSVTS, Košice (1989), 141-145
• Saxl I., Rataj J.: Anizotropie povrchových trhlin v PZT-keramikách (Anisotropy of superficial cracks in PZT-ceramics). In: Fraktografia '89, Dom techniky ČSVTS, Košice (1989), 451-455
• Lešanovský A., Rataj J.: Determination of compact sets in Euclidean spaces by the volume of their dilation. In: DIANA III, Mathematical Institute, Czechoslovak Academy of Sciences, Prague (1990), 165-177
• Saxl I., Rataj J.: Distances of spherical contact in lattices of figures and lattices of figures with faults. In: Geometrical problems of image processing (U. Eckhardt, A.Hübler, W.Nagel & G.Werner eds.), Research in Informatics 4, Akademie-Verlag, Berlin (1991), 179-184
• Rataj J.: Flat section formulae in integral geometry. In: Proc. S4G (International Conference on Stereology, Spatial Statistics and Stochastic Geometry), Union of Czech Mathematicians and Physicists, Prague 1999, 31-38
• Černý R., Rataj J.: How big is the Wiener sausage? In: Proc. S4G (International Conference on Stereology, Spatial Statistics and Stochastic Geometry), Union of Czech Mathematicians and Physicists, Prague 2006, 75-80
• Rataj J.: On estimation of boundary length and curvature densities for planar stationary random sets. In: Stereology and Image Analysis, ECS 10 - Proceedings (V. Capasso et al. Eds.), The Miriam Project Series, Esculapio Pub. Co., Bologna, Italy 2009 (electronic)
  

Theses:

• Rataj J.: Ortogonální pravděpodobnostní jádra [Orthogonal Transition Kernels]. Diploma Thesis, Faculty of Mathematics and Physics, Charles University, Prague (1985)
• Rataj J.: Charakterizace geometrických struktur v euklidovském prostoru [Characterization of Geometrical structures in Euclidean Spaces]. Ph.D. Thesis, Matematical Institute, Academy of Sciences of the Czech Republic, Prague (1991)
• Rataj J.: Translative and kinematic integral geometry for non-smooth bodies. Habilitation Thesis, Faculty of Mathematics and Physics, Charles University, Prague 1999