Dan Mangoubi's Home Page


Dan Mangoubi

Einstein Institute of Mathematics, Edmond J. Safra campus, The Hebrew University, Jerusalem 9190401, Israel Email: firstname.lastname AT mail.huji.ac.il Tel: +972-2-6584145 Fax: +972-2-5630702

Research Interests

Spectral Geometry, Geometry of Eigenfunctions, Harmonic functions - continuous and discrete, Analysis & PDEs.

New Book

(with M. Levitin, I. Polterovich), Topics in spectral geometry, Grad. Stud. Math. 237, American Mathematical Society, Providence, RI, 2023, xviii+325 pp. preliminary version

Preprints

(with D. Rosenblatt) An improved multiplicity bound for eigenvalues of the clamped disk, arXiv:2411.07564.

Papers published or accepted

(with P. Charron) The inner radius of nodal domains in high dimensions, Adv. Math. 452 (2024), Paper No. 109787, 17 pp. , arXiv:2306.00159.

(with A. Weller Weiser) A note on the semiclassical measure at singular points of the boundary of the Bunimovich stadium, Ann. Inst. Fourier (Grenoble) 74 (2024), no. 1, 367–375, arXiv:2206.06624.

(with G. Lippner, Z. McGuirk, R. Yovel) Strong convexity for harmonic functions on compact symmetric spaces, Proc. Amer. Math. Soc. 150 (2022), no. 4, 1613-1622, arXiv:2103.06904.

(with S. Chanillo, A. Logunov, E. Malinnikova) Local version of Courant's nodal domain theorem, J. Differential Geom. 126 (2024), no. 1, 49–63, arXiv:2008.00677.

(with Y. Lvovsky) Bounded multiplicity for eigenvalues of a circular vibrating clamped plate, J. Differential Geom. 121 (2022), no. 2, 369-383, arXiv:1907.12855.

(with A. Weller-Weiser) Harmonic functions vanishing on a cone, Israel J. Math. 230 (2019), no. 2, 563-581, arxiv:1703.09905.

(with G. Lippner) On the sharpness of a three circles theorem for discrete harmonic functions, Int. Math. Res. Not. IMRN 2017, no. 5, 1487-1503, arXiv:1512.03732.

(with G. Lippner) Harmonic functions on the lattice: Absolute monotonicity and propagation of smallness, Duke Math. J. 164 (2015), no. 13, 2577-2595, arXiv:1312.4550.

(with F. Bauer, P. Horn, Y. Lin, G. Lippner, S.-T. Yau) Li-Yau inequality on graphs, J. Differential Geom. 99 (2015), no. 3, 359-405, arXiv:1306.2561.

A gradient estimate for harmonic functions sharing the same zeros, Electron. Res. Announc. Math. Sci. 21 (2014), 62-71, arXiv:1306.0565.

The effect of curvature on convexity properties of harmonic functions and eigenfunctions, J. Lond. Math. Soc. 87 (2013), no. 3, 645-662, arXiv:1112.4352.

A remark on recent lower bounds for nodal sets, Comm. Partial Differential Equations 36 (2011), no. 12, 2208-2212, arXiv:1010.4579.

(with Y. Lin, G. Lippner and S.-T. Yau) Nodal geometry of graphs on surfaces, Discrete Contin. Dyn. Syst. Ser. A 28 (2010), no. 3, 1291-1298, arXiv:1307.3226.

The volume of a local nodal domain, J. Topol. Anal. 2 (2010), no. 2, 259-275, arXiv:0806.3327.

(with D. Jakobson) Tubular neighborhoods of nodal sets and Diophantine approximation, Amer. J. Math. 131 (2009), no. 4, 1109-1135, arXiv:0707.4045.

Local asymmetry and the inner radius of nodal domains, Comm. Partial Differential Equations 33 (2008), no. 9, 1611-1621, arXiv:math/0703663.

On the inner radius of a nodal domain, Canad. Math. Bull. 51 (2008), no. 2, 249-260, arXiv:math/0511329.

Spectral flexibility of symplectic manifolds T²x M, Math. Ann. 341 (2008), no. 1, 1-13, arXiv:math/0508128.

Conformal extension of metrics of negative curvature, J. Anal. Math. 91 (2003), 193-209, arXiv:math/0202249.

Thesis

On the Geometry of the Laplace-Beltrami Operator, Ph.D. Thesis (Technion, 2006) under the direction of Leonid Polterovich and Michael Entov.

Riemann Surfaces and 3-regular Graphs, M.Sc. Thesis (Technion, 2001) under the direction of Robert Brooks, arXiv:math/0202156.

Editorial

I serve on the editorial board of Journal d'Analyse Mathématique