## INFORMATION FOR

# Publications

## Diploma thesis, doctoral thesis, habilitation thesis

- T. Kaiser: Geometrische Eigenschaften von Gevreyfunktionen.

*Diploma thesis,**University of Regensburg, 1999.* - T. Kaiser: Dirichletregularität in polynomial beschränkten o-minimalen Strukturen auf
**R**.*Doctoral thesis, Regensburger Mathematische Schriften 31, 2001.* - T. Kaiser: An o-minimal version of the Riemann Mapping Theorem and the Dirichlet Problem
*.*

Habilitation thesis, University of Regensburg, 2006.

## Published and accepted papers

**[1]** T. Kaiser: Capacity in subanalytic geometry.*Illinois Journal of Mathematics 49 (2005), no. 3, 719-736.***[2]** T. Kaiser: On the convergence of integrals in o-minimal structures on archimedean real closed fields.*Annales Polonici Mathematici 87 (2005), 175-192.***[3]** T. Kaiser: Definability results for the Poisson equation.*Advances in Geometry 6 (2006), no. 4, 627-644. ***[4]** T. Kaiser: Dirichlet regularity in arbitrary o-minimal structures on the field R up to* *dimension 4.

*Mathematische Nachrichten 279 (2006), no. 15, 1669-1683.*

**[5]**T. Kaiser: Capacity density of subanalytic sets in higher dimension.

*Potential Analysis 20 (2007), no. 4, 397 - 407.*

**[6]** T. Kaiser: Real closed graded fields.*Order 24 (2007), no.2, 107 -120. *

**[7]** T. Kaiser: Dirichlet regularity of subanalytic domains.*Transactions of the American Mathematical Society 360 (2008), no. 12, 6573-6594. *

**[8]** T. Kaiser: The Riemann Mapping Theorem for semianalytic domains and* *o-minimality.*Proceedings of the London Mathematical Society (3) 98 (2009), no. 2, 427-444.***[9]** T. Kaiser: The Dirichlet problem in the plane with semianalytic raw data, quasianalyticity * *and o-minimal structures.*Duke Mathematical Journal 147 (2009), no. 2, 285-314.***[10]** T. Kaiser, J.-P. Rolin, P. Speissegger: Transition maps at non-resonant hyperbolie singularities are o-minimal.*Journal für die reine and angewandte Mathematik 636 (2009), 1-45.** ***[11]** T. Kaiser: Asymptotic Behaviour of the Mapping Function at an Analytic Cusp with small Perturbation of Angles.*Computational Methods and Function Theory 10 (2010), no. 1, 35-47.*

**[12] ** T. Kaiser: Harmonic measure and subanalytically tame measures.*Journal of Logic and Analysis 2:7 (2010), 1-29.*

**[13] ** T. Kaiser: Conformal mapping of o-minimal corners.*Analysis 32 (2012), no. 1, 1001-1013.*

**[14] ** T. Kaiser: First order tameness of measures.*Annals of Pure and Applied Logic 163 (2012), no. 12, 1903-1927.*

**[15] ** T. Kaiser: Integration of semialgebraic functions and integrated Nash functions.*Mathematische Zeitschrift 275 (2013), no. 1-2, 349-366.*

**[16] ** M. Knebusch, T. Kaiser: Manis valuations and Prüfer extensions II.*Lecture Notes in Mathematics 2103. Springer 2014, 190 pp.*

**[17] ** T. Kaiser: Multivariate Puiseux rings induced by a Weierstrass system and twisted group rings.*Communications in Algebra 42 (2014), no. 11, 4619-4634.*

**[18]** T. Kaiser: Global complexification of real analytic globally subanalytic functions.*Israel Journal of Mathematics 213 (2016), no. 1, 139-174.*

**[19]**T. Kaiser: R-analytic functions.

*Archive for Mathematical Logic 55 (2016), no. 5-6, 605-623.*

**[20] ** T. Kaiser, S. Lehner: Asymptotic behaviour of the Riemann mapping function at analytic cusps.*Annales Academiae Scientiarum Fennicae Mathematica 42 (2017), no. 1, 3-15, *

**[21] **T. Kaiser: Piecewise Weierstrass preparation and division for o-minimal holomorphic functions.*Proceedings of the American Mathematical Society 145 (2017), no. 9, 3887-3897.*

**[22]** T. Kaiser: Lebesgue measure and integration theory on non-archimedean real closed fields with archimedean Value group.*Proceedings of the London Mathematical Society 116 (2018), no. 2, 209-247.*

## Other publications

- A.-M. Schwarz, M. Brandl, T. Kaiser, A. Patzmann: Interactive mathematical maps for defragmentation.

T. Pooley and G. Guendet (Eds.) (2017).*"Proceedings of the Tenth Congress of the European Society for Research in Mathematics Education (CERME10, February 1-5, 2017)". Dublin, Ireland: DCU Institute of Education and ERME, 2292-2293.*

- T. Kaiser, J. Pila, P. Speissegger, A. Wilkie: O-Minimality and its Applications to Number Theory and Analysis.

Oberwolfach Reports 14 (2017), no. 2, 1349-1420.

## Submitted papers and preprints

- T. Kaiser, P. Speissegger: Analytic continuation of log-exp-analytic germs, 52 pp.
*Submitted*. - T. Kaiser, J. Ruppert: Asymptotics of parameterized exponential integrals given by Brownian motion on globally subanalytic sets, 21 pp.
*Submitted.* - T. Kaiser: Logarithms, constructible functions and integration on non-archimedean models of the theory of the real field with restricted analytic functions with value group of finite archimedean rank, 26 pp.
*Submtted.* - Z. Galal, T. Kaiser, P. Speissegger: Ilyashenko algebras based on transserial asymptotic expansions, 67 pp.
*Submitted.*

## Papers in preparation

- T. Kaiser: Multivariate measure and integration theory on arbitrary real closed fields and on the surreals.
- T. Kaiser: Integration on Nash manifolds over real closed fields and Stokes' theorem.
- T. Kaiser: Arc invariants and Lebesgue zeta functions.
- T. Kaiser, N. Schwartz: Homogeneous rings and their real spectra.