David Preiss Emeritus Professor of Mathematics Email: D dot Preiss at warwick dot ac dot uk

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Research Interests:

Mathematical analysis

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Selected recent publications:

Preiss, D., Kenig, C., and Toro, T., Boundary structure and size in terms of interior and exterior harmonic measures in higher dimensions. J. Amer. Math. Soc., 22 (2009), 771-796.

Preiss, D., Tolsa, X., and Toro, T., On the smoothness of Hölder doubling measures. Calc. Var. Partial Differential Equations, 35 (2009), no. 3, 339-363.

Lindenstrauss, J., Preiss D., and Tišer J. Fréchet differentiability of Lipschitz functions via a variational principle. J. Eur. Math. Soc., 12 (2010), no. 2, 385-412.

Preiss D. Tilings of Hilbert spaces. Mathematika, 56 (2010), 217-230.

Preiss, D., and Gratwick, R., A one-dimensional variational problem with continuous Lagrangian and singular minimizer. Arch. Ration. Mech. Anal., 202 (2011), no. 1, 177-211.

Alberti, G., Csornyei M., Preiss D., and Winter S. Differentiability of Lipschitz functions, structure of null sets, and other problems. In Proceedings of the International Congress of Mathematicians 2010, pp 1379-1394. World Scientific Publishing 2011.

Lindenstrauss, J., Preiss D., and Tišer J. Fréchet differentiability of Lipschitz functions and porous sets in Banach spaces. Annals of Mathematics Studies; no. 179. Princeton University Press 2012.

Preiss D., and Speight G. Differentiability of Lipschitz Functions in Lebesgue Null Sets. Inventiones Mathematicae, 199 (2015), no. 2, 517-559.

Maleva O. and Preiss D. Directional upper derivatives and the chain rule formula for locally Lipschitz functions on Banach spaces. Trans. Am. Math. Soc. 368 (2016), No. 7, 4685-4730.

Doležal M., Preiss D. and Zelený M. Infinite games and σ-porosity. Isr. J. Math. 215 (2016), No. 1, 441-457.

Maleva O. and Preiss D. Cone unrectifiable sets and non-differentiability of Lipschitz functions. Isr. J. Math. 232 (2019), No. 1, 75-108.

Preiss D., Riss E. and Tišer J. A set of positive Gaussian measure with uniformly zero density everywhere. J. Eur. Math. Soc. (JEMS) 23 (2021), No. 7, 2439-2466.

Ives D. and Preiss, D. Solution to a problem of Nirenberg concerning expanding maps. Proc. Am. Math. Soc. 149 (2021), No. 1, 301-310.