Publications

Articles and Preprints

  1. Noncompact self-shrinkers for mean curvature flow with arbitrary genus
    Joint with Huy Nguyen and Mario Schulz
    Preprint 2021, submitted.
    [ArXiv]

  2. Gaussian upper bounds for the heat kernel on evolving manifolds
    Joint with Louis Yudowitz
    Preprint 2020, submitted. [
    ArXiv]

  3. A local singularity analysis for the Ricci flow and its applications to Ricci flows with bounded scalar curvature
    Joint with Gianmichele Di Matteo
    Calc Var. (2022) 61:65 [
    ArXiv | Journal version]

  4. Bubbling analysis and geometric convergence results for free boundary minimal surfaces
    Joint with Lucas Ambrozio, Alessandro Carlotto, and Ben Sharp
    J. Éc. Polytech. Math. 6 (2019), 621-664 [
    ArXiv | Journal version]

  5. Geometric convergence results for closed minimal surfaces via bubbling analysis
    Joint with Lucas Ambrozio, Alessandro Carlotto, and Ben Sharp
    Calc Var. (2022) 61:25 [ArXiv | Journal version]

  6. The moduli space of two-convex embedded tori
    Joint with Robert Haslhofer and Or Hershkovits
    Int. Math. Res. Not. IMRN 2019, No. 2 (2019), 392-406 [
    ArXiv | Journal version]

  7. The higher-dimensional Chern-Gauss-Bonnet formula for singular conformally flat manifolds
    Joint with Huy Nguyen
    J. Geom. Anal. 29, No. 2 (2019), 1043–1074 [
    ArXiv | Journal version]

  8. The moduli space of two-convex embedded spheres
    Joint with Robert Haslhofer and Or Hershkovits
    J. Diff. Geom. 118, No. 2 (2021), 189-221 [
    ArXiv | Journal version]

  9. Qualitative and quantitative estimates for minimal hypersurfaces with bounded index and area
    Joint with Ben Sharp
    Trans. Amer. Math. Soc. 370 (2018), 4373-4399 [
    ArXiv | Journal version]

  10. Smooth long-time existence of Harmonic Ricci Flow on surfaces
    Joint with Melanie Rupflin
    J. Lon. Math. Soc. 95 (2017), 277-304 [
    ArXiv | Journal version]

  11. The Chern-Gauss-Bonnet formula for singular non-compact four-dimensional manifolds
    Joint with Huy Nguyen
    Commun. Anal. Geom. 27, No. 8 (2019), 1697-1736 [
    ArXiv | Journal version]

  12. A note on the compactness theorem for 4d Ricci shrinkers
    Joint with Robert Haslhofer
    Proc. Amer. Math. Soc. 143, No. 10 (2015), 4433-4437 [
    ArXiv | Journal version]

  13. Dynamical stability and instability of Ricci-flat metrics
    Joint with Robert Haslhofer
    Math. Ann. 360 (2014), 547-553 [
    ArXiv | Journal version]

  14. Perelman's entropy functional at Type I singularities of the Ricci flow
    Joint with Carlo Mantegazza
    J. Reine Ang. Math. (Crelle) 703 (2015), 173-199 [
    ArXiv | Journal version]

  15. A compactness theorem for complete Ricci shrinkers
    Joint with Robert Haslhofer
    Geom. Funct. Anal. 21 (2011), 1091-1116 [
    ArXiv | Journal version]

  16. On Type I singularities in Ricci flow
    Joint with Joerg Enders and Peter Topping
    Commun. Anal. Geom. 19, No. 5 (2011), 905-922 [
    ArXiv | Journal version]

  17. Ricci flow coupled with harmonic map flow
    Ann. Sci. Ec. Norm. Sup. 45, fascicule 1 (2012), 101-142 [
    ArXiv | Journal version]

  18. Monotone volume formulas for geometric flows
    J. Reine Ang. Math. (Crelle) 643 (2010), 39-57 [
    ArXiv | Journal version]

Monographs

  1. Ricci flow coupled with harmonic map heat flow (PhD Thesis)
    Diss. ETH Nr. 18290, (2009) [
    ETH E-Collection]

  2. Differential Harnack inequalities and the Ricci flow (Book)
    EMS Series Lect. Math. (2006) [
    Publisher website]

Conference Reports

  1. Harmonic Ricci Flow on surfaces
    Oberwolfach Reports, No. 27, Vol. 13, Issue 2 (2016), 1526-1528 [
    Workshop website]

  2. Dynamical stability and instability of Ricci-flat metrics
    Oberwolfach Reports, No. 37, Vol. 10, Issue 3 (2013), 2131-2132 [
    Workshop website]

  3. Finite time singularities of the Ricci flow
    Oberwolfach Reports, No. 26, Vol. 9, Issue 2 (2012), 1604-1606 [
    Workshop website]

  4. The standard solution for surgery
    Oberwolfach Reports, No. 46, Vol. 5, Issue 4 (2008), 2643-2644 [
    Workshop website]

  5. Monotone volume formulas for geometric flows
    Oberwolfach Reports, No. 27, Vol. 5, Issue 2 (2008), 1502-1504 [
    Workshop website]