Publications of Zbigniew Błocki

Lecture notes


• pdf Z. Błocki, Rearrangements and the Monge-Ampère equations, preprint
  
• pdf Z. Błocki, W. Zwonek, Generalizations of the higher dimensional Suita conjecture and its relation with a problem of Wiegerinck, Journal of Geometric Analysis 30 (2020), 1259-1270
  
• pdf Z. Błocki, On the Monge-Ampère operator for quasi-plurisubharmonic functions with analytic singularities, Bulletin of the London Mathematical Society 51 (2019), 431-435
  
• pdf M. Andersson, Z. Błocki, E. Wulcan, On a Monge-Ampère operator for plurisubharmonic functions with analytic singularities, Indiana University Mathematics Journal 68 (2019), 1217-1231.
  
• pdf Z. Błocki, W. Zwonek, One dimensional estimates for the Bergman kernel and logarithmic capacity, Proceedings of the American Mathematical Society 146 (2018), 2489-2495
  
• pdf Z. Błocki, Suita Conjecture from the one-dimensional viewpoint, in Analysis Meets Geometry: A Tribute to Mikael Passare, eds. M. Andersson, J. Boman, C. Kiselman, P. Kurasov, R. Sigurdsson, Trends in Mathematics, pp. 127-133, Springer, 2017
  
• pdf Z. Błocki, W. Zwonek, Suita conjecture for some convex ellipsoids in ², Experimental Mathematics 25 (2016), 8-16
  
• pdf Z. Błocki, On Nazarov's complex analytic approach to the Mahler conjecture and the Bourgain-Milman inequality, in Complex Analysis and Geometry: KSCV10, Gyeongju, Korea, August 2014, eds. F. Bracci, J. Byun, H. Gaussier, K. Hirachi, K.-T. Kim, N. Shcherbina, Springer Proceedings in Mathematics & Statistics, pp. 89-98, Springer, 2015
  
• pdf Z. Błocki, W. Zwonek, Estimates for the Bergman kernel and the multidimensional Suita conjecture, New York Journal of Mathematics 21 (2015) 151-161
  
• pdf Z. Błocki, Cauchy-Riemann meet Monge-Ampère, Bulletin of Mathematical Sciences 4 (2014), 433-480
  
• pdf Z. Błocki, Bergman kernel and pluripotential theory, in Analysis, complex geometry, and mathematical physics: in honor of Duong H. Phong, eds. P. M. N. Feehan, J. Song, B. Weinkove, R. A. Wentworth, Contemporary Mathematics 644, pp. 1-10, American Mathematical Society, 2015
  
• pdf Z. Błocki, A lower bound for the Bergman kernel and the Bourgain-Milman inequality, Geometric Aspects of Functional Analysis, Israel Seminar (GAFA) 2011-2013, eds. B. Klartag, E. Milman, Lecture Notes in Mathematics 2116, pp. 53-63, Springer, 2014
  
• pdf Z. Błocki, Estimates for and optimal constants, in Complex Geometry and Dynamics, The Abel Symposium 2013 , eds. J. E. Fornæss, M. Irgens, E. Fornæss Wold, Abel Symposia, vol. 10, pp. 45-50, Springer, 2015
  
• pdf Z. Błocki, Sz. Pliś, Squares of positive (p,p)-forms, Comptes Rendus Mathématique, Académie des Sciences, Paris, 351 (2013), 27-32
  
• pdf Z. Błocki, Suita conjecture and the Ohsawa-Takegoshi extension theorem, Inventiones Mathematicae 193 (2013), 149-158
  
• pdf Z. Błocki, On the Ohsawa-Takegoshi extension theorem, Universitatis Iagiellonicae Acta Mathematica 50 (2012), 53-61
  
• pdf Z. Błocki, The complex Monge-Ampère equation in Kähler geometry, course given at CIME Summer School in Pluripotential Theory, Cetraro, Italy, July 2011, eds. F. Bracci, J. E. Fornæss, Lecture Notes in Mathematics 2075, pp. 95-142, Springer, 2013
  
• pdf Z. Błocki, The Calabi-Yau theorem, course given at the Winter School in Complex Analysis, Toulouse, January 2005, appeared in "Complex Monge-Ampère equations and geodesics in the space of Kähler metrics", ed. V. Guedj, Lecture Notes in Mathematics 2038, pp. 201-227, Springer, 2012
  
• pdf Z. Błocki, On the uniform estimate in the Calabi-Yau theorem, II, Science China Mathematics, 54 (2011), 1375-1377
  
• pdf Z. Błocki, S.Dinew, A local regularity of the complex Monge-Ampère equation, Mathematische Annalen 351 (2011), 411-416
  
• pdf Z. Błocki, A.Edigarian, J.Siciak, On the product property for the transfinite diameter, Annales Polonici Mathematici 101 (2011), 209-214
  
• pdf Z. Błocki, On geodesics in the space of Kähler metrics, Proceedings of the "Conference in Geometry" dedicated to Shing-Tung Yau (Warsaw, April 2009), in "Advances in Geometric Analysis", ed. S. Janeczko, J. Li, D. Phong, Advanced Lectures in Mathematics 21, pp. 3-20, International Press, 2012
  
• pdf Z. Błocki, A gradient estimate in the Calabi-Yau theorem, Mathematische Annalen 344 (2009), 317-327
  
• pdf Z. Błocki, A note on maximal plurisubharmonic functions, Proceedings of the Conference "Actual Problems of Complex Analysis", Khiva City, Uzbekistan, 2008, Uzbek Mathematical Journal 1 (2009), 28-32
  
• pdf Z. Błocki, Some applications of the Ohsawa-Takegoshi extension theorem, Expositiones Mathematicae 27 (2009), 125-135
  
• pdf Z. Błocki, Remark on the definition of the complex Monge-Ampère operator, Proceedings of the Conference "Functional Analysis and Complex Analysis", Istanbul 2007, Contemporary Mathematics 481, pp. 17-21, American Mathematical Society, 2009
  
• pdf Z. Błocki, The complex Monge-Ampère equation in Kähler geometry, Proceedings of the 2nd Forum of Polish Mathematicians, Częstochowa, 2008, Prace Naukowe Instytutu Matematyki i Informatyki Politechniki Częstochowskiej 2(7) (2008), 5-13
  
• pdf Z. Błocki, On uniqueness of the complex Monge-Ampère equation on compact Kähler manifolds, Institut Mittag-Leffler, Report No. 1, 2007/2008, spring (this paper will not be published elsewhere)
  
• pdf Z. Błocki, Defining nonlinear elliptic operators for non-smooth functions, Complex Analysis and Digital Geometry, Proceedings from the Kiselmanfest, 2006, ed. M. Passare, Acta Universitatis Upsaliensis, vol. 86, pp. 111-124, Uppsala, 2009
  
• pdf Z. Błocki, A Bergman kernel in ⁿ, holomorphic functions, and related non-associative algebras, International Journal of Mathematics 18 (2007), 1113-1132
  
• pdf Z. Błocki, S. Kołodziej, On regularization of plurisubharmonic functions on manifolds, Proceedings of the American Mathematical Society 135 (2007), 2089-2093
  
• pdf Z. Błocki, Some estimates for the Bergman kernel and metric in terms of logarithmic capacity, Nagoya Mathematical Journal 185 (2007), 143-150
  
• pdf Z. Błocki, The Bergman kernel and pluripotential theory, Potential Theory in Matsue, 2004, pp. 1-9, Advanced Studies in Pure Mathematics, 44, Mathematical Society of Japan, Tokyo, 2006
  
• pdf Z. Błocki, The domain of definition of the complex Monge-Ampère operator, American Journal of Mathematics 128 (2006), 519-530
  
• pdf Z. Błocki, On uniform estimate in Calabi-Yau theorem, Proceedings of SCV2004, Beijing, Science in China Series A Mathematics 48 Supp. (2005), 244-247
  
• pdf Z. Błocki, Weak solutions to the complex Hessian equation, Annales de l'Institut Fourier 55 (2005), 1735-1756
  
• pdf Z. Błocki, The Bergman metric and the pluricomplex Green function, Transactions of the American Mathematical Society 357 (2005), 2613-2625
  
• pdf Z. Błocki, A note on the Hörmander, Donnelly-Fefferman, and Berndtsson L²-estimates for -operator, Annales Polonici Mathematici 84 (2004), 87-91
  
• pdf Z. Błocki, On the definition of the Monge-Ampère operator in ², Mathematische Annalen 328 (2004), 415-423
  
• pdf Z. Błocki, Uniqueness and stability for the Monge-Ampère equation on compact Kähler manifolds, Indiana University Mathematics Journal 52 (2003), 1697-1702
  
• pdf Z. Błocki, Interior regularity of the degenerate Monge-Ampère equation, Bulletin of the Australian Mathematical Society 68 (2003), 81-92
  
• pdf Z. Błocki, Regularity of the degenerate Monge-Ampère equation on compact Kähler manifolds, Mathematische Zeitschrift 244 (2003), 153-161
  
• pdf Z. Błocki, On the Darboux equation, Universitatis Iagiellonicae Acta Mathematica 39 (2001), 87-90
  
• pdf Z. Błocki, Regularity of the pluricomplex Green function with several poles, Indiana University Mathematics Journal 50 (2001), 335-351
  
• pdf Z. Błocki, Interior regularity of the complex Monge-Ampère equation in convex domains, Duke Mathematical Journal 105 (2000), 167-181
  
• pdf Z. Błocki, The C^1,1 regularity of the pluricomplex Green function, Michigan Mathematical Journal 47 (2000), 211-215
  
• pdf Z. Błocki, Equilibrium measure of a product subset of ⁿ, Proceedings of the American Mathematical Society 128 (2000), 3595-3599
  
• pdf Z. Błocki, On the regularity of the complex Monge-Ampère operator, Contemporary Mathematics 222, Complex Geometric Analysis in Pohang, ed. K.-T.Kim, S.G.Krantz, pp.181-189, American Mathematical Society, 1999
  
• pdf Z. Błocki, P.Pflug, Hyperconvexity and Bergman completeness, Nagoya Mathematical Journal 151 (1998), 221-225
  
• pdf Z. Błocki, Regularity of the fundamental solution for the Monge-Ampère operator, Pitman Research Notes in Mathematics Series 384, Progress in partial differential equations, Pont-a-Mousson 1997, vol.1, pp.40-45, Addison Wesley Longman, 1998
  
• pdf Z. Błocki, J. Thorbiornson, On the fundamental solution for the real Monge-Ampère operator, Mathematica Scandinavica 83 (1998), 309-319
  
• pdf Z. Błocki, S.Kołodziej, N. Levenberg, Extremal functions and equilibrium measures for Borel sets, Bulletin of the Polish Academy of Sciences 45 (1997), 291-296
  
• pdf Z. Błocki, Smooth exhaustion functions in convex domains, Proceedings of the American Mathematical Society 125 (1997), 477-484
  
• pdf Z. Błocki, The complex Monge-Ampère operator in hyperconvex domains, Annali della Scuola Normale Superiore di Pisa 23 (1996), 721-747
  
• pdf Z. Błocki, On the L^p-stability for the complex Monge-Ampère operator, Michigan Mathematical Journal 42 (1995), 269-275
  
• pdf Z. Błocki, Estimates for the complex Monge-Ampère operator, Bulletin of the Polish Academy of Sciences 41 (1993), 151-157
  
• pdf Z. Błocki, An elementary proof of the McCoy theorem, Universitatis Iagiellonicae Acta Mathematica 30 (1993), 215-218
  
• pdf Z. Błocki, Singular sets of separately analytic functions, Annales Polonici Mathematici 56 (1992), 219-225
  
• Z. Błocki, A constant in pluripotential theory, Annales Polonici Mathematici 56 (1992), 213-217