Dr Julian Scheuer
Lecturer
- scheuerj@cardiff.ac.uk
- 5.53, Abacws, Senghennydd Road, Cathays, Cardiff, CF24 4AG
Overview
I am a german mathematician specialized in Analysis and Geometry. After completion of my undergraduate and doctoral education in Heidelberg, Germany, I have worked as a postdoc at various places in Germany and the United States.
Biography
Education
- July 2018: Habilitation in mathematics, University of Freiburg, Germany.
- Feb. 2013: PhD in mathematics under supervision of Prof. Dr. Claus Gerhardt, University of Heidelberg, Germany.
- Apr. 2005-Oct. 2009: Studies of Mathematics and Economics (Diplom), University of Heidelberg, Germany.
Employments
- From July 2020: Lecturer for Analysis, School of Mathematics, Cardiff University.
- Apr. 2019-Sept. 2020: Visiting scholar at Columbia University, New York City, USA. (on leave from Freiburg and Cardiff)
- Apr. 2018-Sept. 2018: Interim professor (W2) at the institute for applied analysis, Universtiy of Ulm, Germany. (on leave from Freiburg)
- Apr. 2015-June 2020: Scientific assistant in the group of Prof. Dr. Ernst Kuwert and Prof. Dr. Guofang Wang, University of Freiburg, Germany.
- Jan. 2014-Mar. 2015: Postdoctoral research position (DFG) in the project "Curvature problems" in Prof. Claus Gerhardt's group, University of Heidelberg, Germany.
- Jan. 2012-Jan. 2014: Doctoral research position (DFG) in the project "Curvature problems" in Prof. Claus Gerhardt's group, University of Heidelberg, Germany.
Publications
2022
- Chen, C., Guan, P., Li, J. and Scheuer, J. 2022. A fully-nonlinear flow and quermassintegral inequalities in the sphere. Pure and Applied Mathematics Quarterly 18(2), pp. 437-461. (10.4310/PAMQ.2022.v18.n2.a4)
- Roesch, H. and Scheuer, J. 2022. Mean curvature flow in null hypersurfaces and the detection of MOTS. Communications in Mathematical Physics 390, pp. 1149-1173. (10.1007/s00220-022-04326-9)
- Scheuer, J., Wang, G. and Xia, C. 2022. Alexandrov-Fenchel inequalities for convex hypersurfaces with free boundary in a ball. Journal of Differential Geometry 120(2), pp. 345-373. (10.4310/jdg/1645207496)
- Bryan, P., Ivaki, M. N. and Scheuer, J. 2022. Christoffel-Minkowski flows. Transactions of the American Mathematical Society
2021
- Scheuer, J. 2021. The Minkowski inequality in De Sitter space. Pacific Journal of Mathematics 314(2), pp. 425-449. (10.2140/pjm.2021.314.425)
- Scheuer, J. and Kuwert, E. 2021. Asymptotic estimates for the Willmore flow with small energy. International Mathematics Research Notices 2021(18), pp. 14252-14266. (10.1093/imrn/rnaa015)
- Bryan, P., Kröner, H. and Scheuer, J. 2021. Li-Yau gradient estimates for curvature flows in positively curved manifolds. Methods and Applications of Analysis 27(4), pp. 341-358. (10.4310/MAA.2020.v27.n4.a2)
- Langford, M. and Scheuer, J. 2021. Concavity of solutions to degenerate elliptic equations on the sphere. Communications in Partial Differential Equations 46(6), pp. 1005-1016. (10.1080/03605302.2020.1857404)
- Lambert, B. and Scheuer, J. 2021. Isoperimetric problems for spacelike domains in generalized Robertson-Walker spaces. Journal of Evolution Equations 21(1), pp. 377-389. (10.1007/s00028-020-00584-z)
- Bryan, P., Ivaki, M. N. and Scheuer, J. 2021. Parabolic approaches to curvature equations. Nonlinear Analysis: Theory, Methods and Applications 203, article number: 112174. (10.1016/j.na.2020.112174)
- Bryan, P., Ivaki, M. N. and Scheuer, J. 2021. Orlicz-Minkowski flows. Calculus of Variations and Partial Differential Equations 60, article number: 41. (10.1007/s00526-020-01886-3)
2020
- Bryan, P., Ivaki, M. N. and Scheuer, J. 2020. Negatively curved three-manifolds, hyperbolic metrics, isometric embeddings in Minkowski space and the cross curvature flow. In: Dearricott, O. et al. eds. Differential Geometry in the Large. Cambridge University Press, pp. 75-97., (10.1017/9781108884136.005)
- Scheuer, J. 2020. Minkowski inequalities and constrained inverse curvature flows in warped spaces. Advances in Calculus of Variations (10.1515/acv-2020-0050)
- Bryan, P., Ivaki, M. N. and Scheuer, J. 2020. Harnack inequalities for curvature flows in Riemannian and Lorentzian manifolds. Journal für die reine und angewandte Mathematik 2020(764), pp. 71-109. (10.1515/crelle-2019-0006)
2019
- Scheuer, J. and Xia, C. 2019. Locally constrained inverse curvature flows. Transactions of the American Mathematical Society 372(10), pp. 6771-6803. (10.1090/tran/7949)
- Kröner, H. and Scheuer, J. 2019. Expansion of pinched hypersurfaces of the Euclidean and hyperbolic space by high powers of curvature. Mathematical News / Mathematische Nachrichten 292(7), pp. 1514-1529. (10.1002/mana.201700370)
- Scheuer, J. 2019. Inverse curvature flows in Riemannian warped products. Journal of Functional Analysis 276(4), pp. 1097-1144. (10.1016/j.jfa.2018.08.021)
- Roth, J. and Scheuer, J. 2019. Explicit rigidity of almost-umbilical hypersurfaces. Asian Journal of Mathematics 22(6), pp. 1075-1088. (10.4310/AJM.2018.v22.n6.a5)
- Bryan, P., Ivaki, M. N. and Scheuer, J. 2019. A unified flow approach to smooth, even Lp-Minkowski problems. Analysis & PDE 12(2), pp. 259-280. (10.2140/apde.2019.12.259)
2018
- Scheuer, J. 2018. Isotropic functions revisited. Archiv der Mathematik 110(6), pp. 591-604. (10.1007/s00013-018-1162-4)
- Bryan, P., Ivaki, M. N. and Scheuer, J. 2018. Harnack inequalities for evolving hypersurfaces on the sphere. Communications in Analysis and Geometry 26(5), pp. 1047-1077. (10.4310/CAG.2018.v26.n5.a2)
2017
- Roth, J. and Scheuer, J. 2017. Pinching of the first eigenvalue for second order operators on hypersurfaces of the Euclidean space. Annals of Global Analysis and Geometry 51(3), pp. 287-304. (10.1007/s10455-016-9535-z)
- Lambert, B. and Scheuer, J. 2017. A geometric inequality for convex free boundary hypersurfaces in the unit ball. Proceedings of the American Mathematical Society 145(9), pp. 4009-4020. (10.1090/proc/13516)
- Scheuer, J. 2017. The inverse mean curvature flow in warped cylinders of non-positive radial curvature. Advances in Mathematics 306, pp. 1130-1163. (10.1016/j.aim.2016.11.003)
2016
- Scheuer, J. 2016. Pinching and asymptotical roundness for inverse curvature flows in Euclidean space. Journal of Geometric Analysis 26(3), pp. 2265-2281. (10.1007/s12220-015-9627-1)
- Lambert, B. and Scheuer, J. 2016. The inverse mean curvature flow perpendicular to the sphere. Mathematische Annalen 364, pp. 1069-1093. (10.1007/s00208-015-1248-2)
- Makowski, M. and Scheuer, J. 2016. Rigidity results, inverse curvature flows and Alexandrov-Fenchel type inequalities in the sphere. The Asian Journal of Mathematics 20(5), pp. 869. (10.4310/AJM.2016.v20.n5.a2)
2015
- Scheuer, J. 2015. Quantitative oscillation estimates for almost-umbilical closed hypersurfaces in euclidean space. Bulletin of the Australian Mathematical Society 92(1), pp. 133-144. (10.1017/S0004972715000222)
- Scheuer, J. 2015. Non-scale-invariant inverse curvature flows in hyperbolic space. Calculus of Variations and Partial Differential Equations 53(1-2), pp. 91-123. (10.1007/s00526-014-0742-9)
- Scheuer, J. 2015. Gradient estimates for inverse curvature flows in hyperbolic space. Geometric Flows 1(1) (10.1515/geofl-2015-0002)
Teaching
Academic Year 2021/22
Autumn Semester
MA3018: Measure Theory
For details on my teaching before I came to Cardiff please see my personal webpage.
Research interests
All my papers (journal publications and preprints) are available at arXiv.org.
Here are reviews of my papers at mathscinet.ams.org.
Funding
My research has partially been funded by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) within two projects on curvature flows:
- "Harnack inequalities for curvature flows and applications", 2016-2019, gepris:319506420
- "Quermassintegral preserving local curvature flows", 2019-2020, gepris:400729345
Visibility
Over the past years I have presented my work at various places, including Harvard, Rutgers, Columbia (USA), McGill (Canada), Warwick (UK), Macquarie University Sydney (Australia) and Xiamen (China).
For a full list of talks and attended conferences see my personal webpage.
Supervision
PhD project:
Currently I am supervising Ms. Prachi Sahjwani on her journey towards a PhD. Her project is called "Stability in physical systems governed by curvature quantities", funded by EPSRC.
Undergraduate Project:
I am supervising a year-4 undergraduate project on applied measure theory. We investigate the analytical properties of fractals (such as the Mandelbrot set) with tools from measure theroy and analysis.
For interested prospective students:
In general I am interested in supervising PhD students in the areas of:
- Partial differential equations, with possible applications in
- Geometric evolution equations (mean curvature flow, Ricci flow and their friends)
- Hypersurface geometry (Stability of soap bubbles, theory of convex bodies, isoperimetric inequalities)
- Lorentz geometry and general relativity
Past projects
- Project leader of the project "Harnack inequalities for curvature flows and applications", funded by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG), 2016-2019, gepris:319506420