You are here: Home Group members Group leader: Prof. Dr. Ulrich Menne

Group leader: Prof. Dr. Ulrich Menne

 

All information on this page dates 31 March 2017.

Current information is available at my personal page at the University of Zurich.

 

Contact data

Email: firstname.lastname@aei.mpg.de or firstname.lastname@uni-potsdam.de
Phone: +49 (0) 331 567-7355 (AEI) or +49 (0) 331 977-1181 (UP)
Office: 2.32 (AEI) or 1.08.1.37 (UP)
Postal address at AEI: Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Am Mühlenberg 1, D-14476 Potsdam, Germany

Research interests

My research pertains to the calculus of variations and to elliptic partial differential equations (PDEs). The common theme of my contributions is geometric measure theory – the natural language for many geometric variational problems. For instance, for generalized submanifolds with mean curvature (and integer multiplicity), I proved the existence of a geodesic distance and a second fundamental form, and laid the foundation to study PDEs thereon (see publications no. 4, 6, and 8).

Publications

The five most important contributions marked with an arrow (→). The number of total pages is shown in bold if and only if it is 50 pages or more. Publications are listed in logical order.

  1. Some applications of the isoperimetric inequality for integral varifolds, 23 pages.
    Adv. Calc. Var., 2(3):247–269, 2009.
    DOI: 10.1515/ACV.2009.010. ArXiv: 0808.3652v1 [math.DG].

  2. Note: The last two sentences of Remark 2.7 therein should have referred to integral varifolds, see Remark 7.7 in Publiction no. 6.

  3. A Sobolev Poincaré type inequality for integral varifolds, 40 pages.
    Calc. Var. Partial Differential Equations, 38(3-4):369–408, 2010.
    DOI: 10.1007/s00526-009-0291-9. ArXiv: 0808.3660v2 [math.DG].

  4. → Decay estimates for the quadratic tilt-excess of integral varifolds, 83 pages.
    Arch. Ration. Mech. Anal., 204(1):1–83, 2012.
    DOI: 10.1007/s00205-011-0468-1. ArXiv: arXiv:0909.3253v3 [math.DG].

  5. → Second order rectifiability of integral varifolds of locally bounded first variation, 55 pages.
    J. Geom. Anal., 23(2):709–763, 2013.
    DOI: 10.1007/s12220-011-9261-5. ArXiv: arXiv:0808.3665v3 [math.DG].

  6. A sharp lower bound on the mean curvature integral with critical power for integral varifolds, 3 pages.
    In abstracts from the workshop held July 22-28, 2012, Organized by Camillo De Lellis, Gerhard Huisken and Robert Jerrard, Oberwolfach Reports. Vol. 9, no. 3, 2012.
    DOI: 10.4171/OWR/2012/36.

  7. → Weakly differentiable functions on varifolds, 112 pages.
    Indiana Univ. Math. J., 65(3):977–1088, 2016.
    DOI: 10.1512/iumj.2016.65.5829. ArXiv: arXiv:1411.3287v1 [math.DG].

  8. Decay rates for the quadratic and super-quadratic tilt-excess of integral varifolds (joint with Sławomir Kolasiński), 56 pages.
    NoDEA Nonlinear Differential Equations Appl., 24, 2017.
    DOI: 10.1007/s00030-017-0436-z. ArXiv: arXiv:1501.07037v2 [math.DG].

  9. → Sobolev functions on varifolds, 50 pages.
    Proc. Lond. Math. Soc. (3), 113(6):725–774, 2016.
    Free access link. DOI: 10.1112/plms/pdw023. ArXiv: arXiv:1509.01178v3 [math.CA].

  10. → Pointwise differentiability of higher order for sets, 33 pages.
    Submitted, 2016.
    ArXiv: arXiv:1603.08587v1 [math.DG].

  11. An isoperimetric inequality for diffused surfaces (joint with Christian Scharrer), 14 pages.
    Kodai Math. J., awaiting publication, 2017.
    ArXiv: 1612.03823v1 [math.DG].

Note: Publications no. 1 and 2 precisely contain the results of my PhD thesis at the University of Tübingen (2008).

The author maintains a list of errata which, apart of one remark in Publication no. 1 (see above), are of typographical nature.