Vlad Yaskin
Department of Math & Stat Sciences
University of Alberta
Phone: (780) 492-0216
Email:

Book

• A.Koldobsky, V.Yaskin, The Interface between Convex Geometry and Harmonic Analysis, CBMS Regional Conference Series, 108, American Mathematical Society, Providence RI, 2008,107 pp.

Papers

• "A generalization of Grünbaum's inequality", (with Brayden Letwin), submitted.

• "Answers to questions of Grünbaum and Loewner", (with Sergii Myroshnychenko and Kateryna Tatarko ), submitted.

• "On separably integrable symmetric convex bodies", (with Bartłomiej Zawalski), Adv. Math., to appear.

• "On the maximal distance between the centers of mass of a planar convex body and its boundary", (with Fedor Nazarov and Dmitry Ryabogin ), Discrete & Computational Geometry, to appear.

• "How far apart can the projection of the centroid of a convex body and the centroid of its projection be?", (with Sergii Myroshnychenko and Kateryna Tatarko ), Math. Ann., to appear.

• "On a uniqueness problem in discrete tomography", (with Golden Sun), Amer. Math. Monthly, to appear.

• "Algebraically integrable bodies and related properties of the Radon transform", (with M. Agranovsky , J. Boman , A. Koldobsky and V. Vassiliev ), in Harmonic Analysis and Convexity, edited by Alexander Koldobsky and Alexander Volberg, Adv. Anal. Geom. 9, De Gruyter, Berlin, 2023, 1-36.

• "Analysis and geometry near the unit ball: proofs, counterexamples, and open questions", (with M. Angeles Alfonseca , Fedor Nazarov , Dmitry Ryabogin ), in Harmonic Analysis and Convexity, edited by Alexander Koldobsky and Alexander Volberg, Adv. Anal. Geom. 9, De Gruyter, Berlin, 2023, 445-468.

• "An analogue of polynomially integrable bodies in even-dimensional spaces", (with M. Agranovsky , A. Koldobsky and D. Ryabogin ), J. Math. Anal. Appl., in press.

• "On a generalization of Busemann's intersection inequality", Journal of Functional Analysis, to appear.

• "A generalization of Winternitz's theorem and its discrete version", (with A. Shyntar), Proc. Amer. Math. Soc. 149 (2021), no. 7, 3089-3104.

• "A solution to the Fifth and the Eighth Busemann-Petty problems in a small neighborhood of the Euclidean ball ", (with M. Angeles Alfonseca , Fedor Nazarov , Dmitry Ryabogin ), Adv. Math. 390 (2021), 28 pp.

• "Unique determination of ellipsoids by their dual volumes", (with Sergii Myroshnychenko and Kateryna Tatarko ) International Mathematics Research Notices, 2022, no. 17, 13569-13589.

• "An extension of polynomial integrability to dual quermassintegrals", International Mathematics Research Notices 13 (2020), 3978-3990.

• "Applications of Grünbaum-type inequalities", (with Matthew Stephen), Trans. Amer. Math. Soc. 372 (2019), 6755-6769.

• "Busemann's intersection inequality in hyperbolic and spherical spaces", (with Susanna Dann and Jaegil Kim), Adv. Math. 326 (2018), 521-560.

• "Grünbaum-type inequality for log-concave functions", (with Mathieu Meyer, Fedor Nazarov, and Dmitry Ryabogin), Bull. Lond. Math. Soc. 50 (2018), 745-752.

• "On polynomially integrable convex bodies", (with Alexander Koldobsky and Alexander Merkurjev), Adv. Math. 320 (2017), 876-886.

• "On sections of convex bodies in hyperbolic space ", (with K.L.H. Hiripitiyage), J. Math. Anal. Appl. 445 (2017), 1394-1409.

• "On the volume of sections of a convex body by cones", (with Matthieu Fradelizi and Mathieu Meyer), Proc. Amer. Math. Soc. 145 (2017), 3153-3164.

• "Distribution functions of sections and projections of convex bodies", (with Jaegil Kim and Artem Zvavitch), J. London Math. Soc. 95 (2017), 52-72.

• "Unique determination of convex lattice sets", (with Dmitry Ryabogin and Ning Zhang), Discrete & Computational Geometry 57 (2017), 582-589.

• "Non-central sections of convex bodies", (with Ning Zhang), Israel J. Math. 220 (2017), 763-790.

• "Stability results for sections of convex bodies", (with Matthew Stephen), Trans. Amer. Math. Soc. 369 (2017), 6239-6261.

• "Thick sections of convex bodies", (with Maryna Yaskina), Advances in Applied Mathematics, 71 (2015), 174-189.

• "Counterexamples to convexity of k-intersection bodies", Proc. Amer. Math. Soc., 142 (2014), 4355-4363.

• "Harmonic Analysis and Uniqueness questions in Convex Geometry", (with Dmitry Ryabogin and Artem Zvavitch), in Recent Advances in Harmonic Analysis (in honor of K. Oskolkov's 65th birthday), Springer Proceedings in Mathematics 25 (2013), 327-337.

• "On counterexamples in questions of unique determination of convex bodies", (with Dmitry Ryabogin), Proc. Amer. Math. Soc. 141 (2013), no. 8, 2869-2874.

• "Detecting symmetry in star bodies", (with Dmitry Ryabogin), J. Math. Anal. Appl., 395 (2012), 509-514.

• "A problem of Klee on inner section functions of convex bodies", (with Richard Gardner, Dmitry Ryabogin, Artem Zvavitch), J. Differential Geom. 91 (2012), 261-279.

• "The geometry of $p$-convex intersection bodies", (with Jaegil Kim and Artem Zvavitch), Advances in Math. 226 (2011), 5320-5337.

• "On perimeters of sections of convex polytopes", J. Math. Anal. Appl. 371, no. 2 (2010), 447-453.

• "Unique determination of convex polytopes by non-central sections", Math. Ann. 349, no. 3 (2011), 647-655.

• "A Fourier transform approach to Christoffel's problem", (with P. Goodey and M. Yaskina), Trans. Amer. Math. Soc., 363 (2011), 6351-6384.

• "On Fourier transform techniques in convex geometry", in Proceedings of the international conference "Geometry 'in large', Topology and Applications" dedicated to the 90-th birthday of A.V.Pogorelov, 152 - 161, Kharkov, Ukraine, October 2010, ACTA.

• "Fourier transforms and the Funck-Hecke theorem in convex geometry", (with P. Goodey and M. Yaskina), J. London Math. Soc. (2) 80 (2009) 388-404.

• "On strict inclusions in hierarchies of convex bodies", Proc. Amer. Math. Soc., 136 (2008), 3281-3291.

• "Modified Shephard's problem on projections of convex bodies", Israel J. Math., 168 (2008), 221-238.

• "Inequalities of the Kahane-Khinchin type and sections of $L_p$-balls", (with A. Koldobsky and A. Pajor), Studia Math. 184 (2008), 217-231.

• "The geometry of $L_0$" , (with N. J. Kalton, A. Koldobsky and M. Yaskina), Canadian J. Math. 59 no. 5 (2007), 1029--1049.

• "A solution to the lower dimensional Busemann-Petty problem in the hyperbolic space" , J. Geom. Anal. 16 (2006), no. 4, 735--745.

• "Centroid bodies and comparison of volumes" , (with M. Yaskina), Indiana Univ. Math. J. 55 (2006), no. 3, 1175--1194.

• "The Busemann-Petty problem in hyperbolic and spherical spaces", Advances in Math. 203 (2006), no. 2, 537--553.

• "Modified Busemann-Petty problem on sections on convex bodies", (with A. Koldobsky and M. Yaskina), Israel J. Math. 154 (2006), 191--208.

• Totally geodesic submanifolds of surfaces with the revolution group $SO(2)\times SO(2)$, Kharkov University Vestnik, 475, (2000), 282--295. (Russian)

• Totally geodesic submanifolds of hypersurfaces of revolution in the Euclidean space, Mat. Fiz. Anal. Geom. 6 (1999), no 1/2, 182--188. (Russian)

  Other writings

• "A guide to Morgan and Shalen", (with S. Dostoglou and M. Yaskina).