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Dr Julian Scheuer

Dr Julian Scheuer


School of Mathematics

5.53, Abacws, Senghennydd Road, Cathays, Cardiff, CF24 4AG


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.



  • 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.


  • 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.











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

I am interested in the theory and applications of geometric evolution equations, such as the mean curvature flow, the inverse mean curvature flow and other fully nonlinear variants. A main motivation lies in their applicability to questions arising from convex geometry, such as generalized isoperimetric inequalities or existence of prescribed curvature measures and also in questions arsing from general relativity, such as Penrose-type inequalities.

All my papers (journal publications and preprints) are available at

Here are reviews of my papers at


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


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.


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