Spectrum of Schrödinger operators under Riemannian coverings and submersions

Liouville type properties of covering spaces

Spectral theory of geometrically finite manifolds

A. Girouard and P. Polymerakis, Large Steklov eigenvalues under volume constraints, preprint, arxiv.org/abs/2403.08925.

W. Ballmann, M. Mukherjee and P. Polymerakis, On the spectrum of certain Hadamard manifolds, SIGMA 19 (2023), 050, 19 pages. (publication)

P. Polymerakis, Normal covering spaces with maximal bottom of spectrum,  J. Geom. Anal. 33, 270 (2023). (publication)

W. Ballmann and P. Polymerakis, Bottom of spectra and coverings of orbifolds, Internat. J. Math. 32 (2021), no. 12, 2140018, 33 pp. (publication)

W. Ballmann and P. Polymerakis, Small eigenvalues of Schrödinger operators over geometrically finite manifolds, to appear in Math. Res. Lett. (arxiv) 

P. Polymerakis, On the Steklov spectrum of covering spaces and total spaces, Ann. Global Anal. Geom. 63 (2023), no. 1, Paper No. 10, 22 pp. (publication)

G. P. Bessa, V. Gimeno and P. Polymerakis, The spectrum of the Laplacian and volume growth of proper minimal submanifolds, Math. Z. 301 (2022), 2761–2770. (publication)

W. Ballmann and P. Polymerakis, On the essential spectrum of differential operators over geometrically finite orbifolds, J. Differential Geom. 127 (2024), no. 1, 1-34.  (publication)

P. Polymerakis, Spectral estimates for Riemannian submersions with fibers of basic mean curvature, J. Geom. Anal. 31 (2021), no. 10, 9951-9980. (publication)

W. Ballmann and P. Polymerakis, Equivariant discretizations of diffusions and harmonic functions of bounded growth, Israel J. Math 246 (2021), no. 1, 32 pp. (publication)

W. Ballmann and P. Polymerakis, Bottom of spectra and coverings, Surv. Differ. Geom. 23 (2020), 1-33. (publication)

P. Polymerakis, Spectral estimates and discreteness of spectra under Riemannian submersions, Ann. Global Anal. Geom. 57 (2020), no. 2, 349-363. (publication)

P. Polymerakis, Positive harmonic functions on groups and covering spaces, Adv. Math. 379 (2021), 107552, 8 pp. (publication, corrected version)

P. Polymerakis, On the strong Liouville property of covering spaces, Potential Anal. 59 (2023), 1449–1455. (publication)

W. Ballmann and P. Polymerakis, Equivariant discretizations of diffusions, random walks, and harmonic functions, Enseign. Math. 67 (2021), no. 3-4, 331-367. (publication, corrected version)

P. Polymerakis, Coverings preserving the bottom of the spectrum, J. Spectr. Theory 12 (2022), no. 3, pp. 993–1022. (publication)

W. Ballmann, H. Matthiesen and P. Polymerakis, Bottom of spectra and amenability of coverings, Geometric Analysis, Prog. Math., vol. 333, Birkhäuser, 2020, pp. 17-35. (publication)

P. Polymerakis, On the spectrum of differential operators under Riemannian coverings, J. Geom. Anal. 30 (2020), no. 3, 3331-3370. (publication)

W. Ballmann, H. Matthiesen and P. Polymerakis, On the bottom of spectra under coverings, Math. Z. 288 (2018), no. 3-4, 1029-1036. (publication)