Publications:
An end to end gluing construction for metrics of constant Q-curvature. (joint with A. S. Aiken, R. Caju and A. Silva Santos) preprint. arxiv version
Quantitative stability of the total Q-curvature functional near minimizing metrics. (joint with J. H. Andrade, T. König and J. Wei) preprint. arxiv version
Moduli space theory for complete, constant Q-curvature metrics on finitely punctured spheres. (joint with R. Caju and A. Silva Santos) preprint. arxiv version
Compactness of singular solutions to the sixth order GJMS equation. (joint with J. H. Andrade, J. M do O. and J. Wei), to appear in Math. Ann. arxiv version, journal version
Constant Q-curvature metrics with Delaunay ends: the nondegenerate case. (joint with J. H. Andrade, R. Caju, J. M. do Ó, and A, Silva Santos), Ann. della Scuola Norm. di Pisa. 25 (2024), 965--1031. arxiv version, published version
Compactness within the space of complete, constant Q-curvature metrics on the sphere with isolated singularities. (joint with J. H. Andrade and J. M. do Ó), Int. Math. Res. Not. 2022 (2022), 17,282--17,302. arxiv version, published version
Foliation of an asymptotically flat end by critical capacitors. (joint with M. M. Fall and I. A. Minlend) J. Geom. Anal. 32 (2022), 32 pages. arxiv version, published version
On a fourth order conformal invariant. preprint, arxiv version
On constant Q-curvature metrics with isolated singularities. preprint, arxiv version
On the rate of change of the best constant in the Sobolev inequality. (joint with T. Carroll and M. M. Fall), Math. Nachr. 290 (2017), 2185-2197. arxiv version, published version
Monotonicity of the first Dirichlet eigenvalue of the Laplacian on manifolds with nonpositive curvature. (joint with T. Carroll), Indiana Univ. Math. J. 65 (20016), 353-376. arxiv version, published version
A reverse Hölder inequality for extremal Sobolev functions. (joint with T. Carroll), Potential Anal. 42 (2015), 283-292. arxiv version, published version
A numerical investigation of level sets of extremal Sobolev functions. (joint with S. Junke), Involve 8 (2015), 787-799. arxiv version, published version
An isoperimetric inequality for extremal Sobolev functions. (joint with T. Carroll), RIMS Kôkyûrroku Bessatsu B43 (2013), 1-16. arxiv version, published version
Two isoperimetric inequalities for the Sobolev constant. (joint with T. Carroll), Z. Angew. Math. Phys. 63 (2012), 855-863. arxiv version, published version
Isoperimetric inequalities and variations on Schwarz's Lemma. (joint wiht T. Carroll), arxiv version (subsumed by the paper in ZAMP).
Interpolating between torsional rigidity and principal frequency. (joint with T. Carroll), J. Math. Anal. Appl. 379 (2011), 818-826. arxiv version, published version
Eigenvalues of Euclidean wedge domains in higher dimensions. Calc. Var. PDE 42 (2011), 93-106. arxiv version, published version
A Payne-Weinberger estimate for wedge domainson spheres, (joint with A. Treibergs), Proc. Amer. Math. Soc. 137 (2009), 2299-2309. arix version, published version
Coplanar k-unduloids are nondegenerate. (joint with K. Große-Brauckmann, N. Korevaar, R. Kusner, and J. Sullivan), Int. Math. Res. Not. 2009 (2009), 3391-3416. arxiv version, published version
A capture problem in Brownian motion and eigenvalues of spherical domains. (joint with A. Treibergs), Trans. Amer. Math. Soc. 361 (2009), 391-405. arxiv version, published version
On the nondegeneracy of constant men curvature surfaces. (joint with N. Korevaar and R. Kusner), Geom. Funct. Anal. 16 (2006), 891-923. arxiv version, published version
An end to end gluing construction for metrics of constant positive scalar curvature. Indiana Univ. Math. J. 52 (2003), 703-726. arxiv version, published version
An end-to-end gluing construction for surfaces of constant mean curvature, PhD dissertation (under the direction of Daniel Pollack), University of Washington, 2001
Slides from recent talks:
Moduli space theory for constant Q-curvature metrics, Banff, Dec. 2024
Stability of the total Q-curvature functional, Hong Kong, Oct. 2024
Gluing constructions of singular constant Q-curvature metrics, Brasilia, Brazil, Sept. 2023
Compactness of constant Q-curvature metrics, Granada, June 2023