## Thesis

- Diploma Thesis: Supersymmetric Wilson Loops in the AdS/CFT correspondence
- PhD Thesis: The Evolution Equations for Dirac-harmonic Maps

## Articles

- BPS Wilson loops in N=4 SYM: Examples on hyperbolic submanifolds of space-time (with Nadav Drukker)
- Arxiv Version
- Published Version:
**Phys. Rev. D 79, Vol. 79, Iss. 10-15 May 2009**

- Magnetic Dirac-harmonic Maps
- Arxiv Version
- Published Version:
**Anal.Math.Phys. (2015) 5:23-37**

- The evolution equations for regularized Dirac-geodesics
- Arxiv Version
- Published Version:
**Journal of Geometry and Physics, Volume 100, February 2016, Pages 1-19**

- Dirac-harmonic maps with torsion
- Arxiv Version
- Published Version:
**Commun. Contemp. Math., 18, 1550064 (2016)**

- On the evolution of regularized Dirac-harmonic maps from closed surfaces
- Arxiv Version
- Published Version:
**Results in Mathematics volume 75, Article number: 57 (2020)**

- Magnetic Geodesics via the Heat Flow (with Florian Hanisch)
- Arxiv Version
- Published Version:
**Asian Journal of Mathematics, Volume 21 (2017), Number 6**

- Some aspects of Dirac-harmonic maps with curvature term
- Arxiv Version
- Published Version:
**Differential Geometry and its Applications, Volume 40, June 2015, Pages 1-13**

- The normalized second order renormalization group flow on closed surfaces
- Arxiv Version
- Published Version:
**Advances in Theoretical and Mathematical Physics, Volume 20 (2016), Number 5, Pages 1167 – 1191**

- Energy estimates for the supersymmetric nonlinear sigma model and applications
- Arxiv Version
- Published Version:
**Potential Anal (2016) 45: 737.**

- An estimate on the nodal set of eigenspinors on closed surfaces
- Arxiv Version
- Published Version:
**Mathematische Zeitschrift, February 2018, Volume 288, Issue 1–2, pp 1–10**

- The heat flow for the full bosonic string
- Arxiv Version
- Published Version:
**Ann Glob Anal Geom (2016) 50: 347** - Some Corrections:
**Ann Glob Anal Geom**

- A note on twisted Dirac operators on closed surfaces
- Arxiv Version
- Published Version:
**Differential Geometry and its Applications, Volume 60, October 2018, Pages 54–65**

- Magnetic geodesics on surfaces with singularities (with Wayne Rossman)
- Arxiv Version
- Published Version:
**Pac. J. Math. Ind. (2017) 9: 3**

- Nonlinear Dirac equations, Monotonicity Formulas and Liouville Theorems
- Arxiv Version
- Published Version:
**Communications in Mathematical Physics, December 2019, Volume 372, Issue 3, pp 733-767**

- The Ricci flow with metric torsion on closed surfaces (with Klaus Kroencke)
- Arxiv Version
- Published Version:
**Journal of Geometric Analysis, July 2017, Volume 27, Issue 3, pp 2098-2117**

- Some Remarks on Energy inequalities for harmonic maps with potential
- Arxiv Version
- Published Version:
**Archiv der Mathematik, August 2017, Volume 109, Issue 2, pp 151–165**

- On the full bosonic string from Minkowski space to Riemannian manifolds
- Arxiv Version
- Published Version:
**Journal of Mathematical Analysis and Applications, Volume 451, Issue 2, 15 July 2017, Pages 858-872**

- On conservation laws for the supersymmetric sigma model
- Arxiv Version
- Published Version:
**Results in Mathematics, December 2017, Volume 72, Issue 4, pp 2181–2201**

- Energy methods for Dirac-type equations in two-dimensional Minkowski space
- Arxiv Version
- Published Version:
**Letters in Mathematical Physics, February 2019, Volume 109, Issue 2, pp 295–325**

- Global existence of Dirac-wave maps with curvature term on expanding spacetimes (with Klaus Kroencke)
- Arxiv Version
- Published Version:
**Calculus of Variations and Partial Differential Equations, Volume 57, Issue 5, October 2018**

- A global weak solution to the full bosonic string heat flow
- Arxiv Version
- Published Version:
**Journal of Evolution Equations, December 2018, Volume 18, Issue 4, pp 1819–1841**

- A Liouville-type Theorem for biharmonic maps between complete Riemannian manifolds with small energies
- Arxiv Version
- Published Version:
**Archiv der Mathematik, September 2018, Volume 111, Issue 3, pp 329–336**

- On interpolating sesqui-harmonic maps between Riemannian manifolds
- Arxiv Version
- Published Version:
**Journal of Geometric Analysis, Volume 30, pages 248-273, 2020**

- Stable cosmological Kaluza-Klein Spacetimes (with David Fajman and Klaus Kroencke)
- Arxiv Version
- Published Version:
**Communications in Mathematical Physics, June 2019, Volume 368, Issue 3, pp 1087–1120**

- A vanishing result for the supersymmetric nonlinear sigma model in higher dimensions
- Arxiv Version
- Published Version:
**Journal of Geometry and Physics, Volume 134, December 2018, Pages 1-10**

- A nonexistence theorem for proper biharmonic maps into general Riemannian manifolds (with Yong Luo)
- Arxiv Version
- Published Version:
**Journal of Geometry and Physics, Volume 148, February 2020, 103557**

- Unique continuation theorems for biharmonic maps (with Cezar Oniciuc)
- Arxiv Version
- Published Version:
**Bulletin of the London Mathematical Society, Volume 51, Issue 4, August 2019, Pages 603-621**

- A structure theorem for polyharmonic maps between Riemannian manifolds
- Arxiv Version
- Published Version:
**Journal of Differential Equations, Volume 273, 5 February 2021, Pages 14-39**

- The stress-energy tensor for polyharmonic maps
- Arxiv Version
- Published Version:
**Nonlinear Analysis, Volume 190, January 2020**

- Higher order energy functionals (with Stefano Montaldo, Cezar Oniciuc and Andrea Ratto)
- Arxiv Version
- Published Version:
**Advances in Mathematics, Volume 370, 26 August 2020, 107236**

- Some analytic results on interpolating sesqui-harmonic maps
- Arxiv Version
- Published Version:
**Annali di Matematica Pura ed Applicata (1923 -), Volume 199, pages 2039–2059 (2020)**

- Dirac-harmonic maps with potential
- Harmonic maps with torsion
- Arxiv Version
- Published Version:
**SCIENCE CHINA Mathematics, Volume 64, pages 1373–1390 (2021)**

- On finite energy solutions of 4-harmonic and ES4-harmonic maps
- Arxiv Version
- Published Version:
**Journal of Geometric Analysis, Volume 31 (2021), no. 8, 8666–8685**

- Unique continuation properties for polyharmonic maps between Riemannian manifolds
(with Stefano Montaldo, Cezar Oniciuc and Andrea Ratto)
- Arxiv Version
- Published Version:
**Canadian Journal of Mathematics**

- Polyharmonic hypersurfaces into pseudo-Riemannian space forms (with Stefano Montaldo, Cezar Oniciuc and Andrea Ratto)
- On the stability of harmonic self-maps of cohomogeneity one manifolds (with Anna Siffert)
- Remarks on polyharmonic curves of constant curvature

**Volker Branding**

**Faculty of Mathematics**

University of Vienna

Oskar-Morgenstern-Platz 1

1090 Vienna

T: +43-1-4277-50780