I. Polterovich

发表

Persistence barcodes and Laplace eigenfunctions on surfaces

L. Polterovich, I. Polterovich, Vukašin Stojisavljević, 2017, Geometriae Dedicata.

Spectral problems with mixed Dirichlet-Neumann boundary conditions: isospectrality and beyond

Dmitry Jakobson, Iosif Polterovich, Michael Levitin, 2004 .

THE STEKLOV SPECTRUM OF CUBOIDS

Iosif Polterovich, Alessandro Savo, Alexandre Girouard, 2017, Mathematika.

How large can the first eigenvalue be on a surface of genus two

N. Nadirashvili, I. Polterovich, N. Nigam, 2005, math/0509398.

Geometric Aspects of Spectral Theory

T. Hoffmann-Ostenhof, I. Polterovich, M. Berg, 2012 .

Coarse nodal count and topological persistence

L. Polterovich, I. Polterovich, Jordan Payette, 2022, 2206.06347.

Sloshing, Steklov and corners: Asymptotics of Steklov eigenvalues for curvilinear polygons

David A. Sher, I. Polterovich, M. Levitin, 2019, Proceedings of the London Mathematical Society.

Isospectral domains with mixed boundary conditions

I. Polterovich, M. Levitin, L. Parnovski, 2005, math/0510505.

Coarse nodal count and topological persistence

L. Polterovich, I. Polterovich, Jordan Payette, 2022, 2206.06347.

How large can the first eigenvalue be on a surface of genus two

N. Nadirashvili, I. Polterovich, N. Nigam, 2005, math/0509398.

Heat invariants of Riemannian manifolds

I. Polterovich, 1999, math/9905073.

Extremal Metric for the First Eigenvalue on a Klein Bottle

N. Nadirashvili, I. Polterovich, D. Jakobson, 2003, Canadian Journal of Mathematics.

Inverse electrostatic and elasticity problems for checkered distributions

I. Polterovich, A. Artemev, L. Parnovski, 2013 .

A Lower Bound for the Remainder in Weyl's Law on Negatively Curved Surfaces

I. Polterovich, D. Jakobson, J. Toth, 2006, math/0612250.

From Agmon–Kannai Expansion to Korteweg–de Vries Hierarchy

I. Polterovich, 1999, solv-int/9905001.

SHAPE OPTIMIZATION FOR LOW NEUMANN AND

I. Polterovich, A. Girouard, 2009 .

Persistence barcodes and Laplace eigenfunctions on surfaces

L. Polterovich, I. Polterovich, Vukašin Stojisavljević, 2018, Geometriae Dedicata.

Explicit Constructions of Universal R‐Trees and Asymptotic Geometry of Hyperbolic Spaces

I. Polterovich, A. Dyubina, 1999, math/9904133.

On the asymptotic geometry of the hyperbolic plane

A. Shnirelman, I. Polterovich, 1998, math/9806106.

On a class of inverse electrostatic and elasticity problems

I. Polterovich, A. Artemev, L. Parnovski, 2012, 1210.0124.

Smooth billiards with a large Weyl remainder

I. Polterovich, Suresh Eswarathasan, J. Toth, 2013, 1304.6440.

Lower bounds for the spectral function and for the remainder in local Weyl’s law on manifolds

I. Polterovich, D. Jakobson, 2005 .

Estimates from Below for the Spectral Function and for the Remainder in Local Weyl’s Law

I. Polterovich, D. Jakobson, 2005, math/0505400.

The Dirichlet-to-Neumann map, the boundary Laplacian, and Hörmander’s rediscovered manuscript

I. Polterovich, M. Levitin, A. Girouard, 2021, Journal of Spectral Theory.

Steklov Spectral Geometry for Extrinsic Shape Analysis

Yu Wang, Mirela Ben-Chen, Justin Solomon, 2017, ACM Trans. Graph..

Nodal length of Steklov eigenfunctions on real-analytic Riemannian surfaces

David A. Sher, I. Polterovich, J. Toth, 2015, Journal für die reine und angewandte Mathematik (Crelles Journal).

Stability of isoperimetric inequalities for Laplace eigenvalues on surfaces

Iosif Polterovich, Daniel L. Stern, Mikhail Karpukhin, 2021, 2106.15043.

Average Growth of the Spectral Function on a Riemannian Manifold

I. Polterovich, Y. Safarov, Hugues Lapointe, 2008, 0803.4171.

Conformally maximal metrics for Laplace eigenvalues on surfaces

N. Nadirashvili, I. Polterovich, A. Penskoi, 2020, Surveys in Differential Geometry.

Heat kernel asymptotics for Laplace type operators and matrix KdV hierarchy

I. Polterovich, 2000, math/0010057.

SPECTRAL GEOMETRY OF THE STEKLOV PROBLEM

Iosif Polterovich, Alexandre Girouard, I. Polterovich, 2014, 1411.6567.

Upper bounds for Steklov eigenvalues on surfaces

Iosif Polterovich, Alexandre Girouard, I. Polterovich, 2012, 1202.5108.

An isoperimetric inequality for Laplace eigenvalues on the sphere

N. Nadirashvili, I. Polterovich, A. Penskoi, 2017, Journal of Differential Geometry.

Pólya’s conjecture for the disk: a computer-assisted proof

David A. Sher, I. Polterovich, M. Levitin, 2022 .

Maximization of the second positive Neumann eigenvalue for planar domains

Iosif Polterovich, Alexandre Girouard, Nikolai Nadirashvili, 2008, 0801.2142.

Pólya’s conjecture for Euclidean balls

David A. Sher, I. Polterovich, M. Levitin, 2022, Inventiones mathematicae.

Combinatorics of the Heat Trace on Spheres

I. Polterovich, 2001, Canadian Journal of Mathematics.

Sloshing, Steklov and corners: Asymptotics of sloshing eigenvalues

Iosif Polterovich, Michael Levitin, Leonid Parnovski, 2017, Journal d'Analyse Mathématique.

Weyl’s Law for the Steklov Problem on Surfaces with Rough Boundary

I. Polterovich, Jean Lagac'e, M. Karpukhin, 2022, Archive for Rational Mechanics and Analysis.

Eigenvalues of a One-Dimensional Dirac Operator Pencil

I. Polterovich, D. Elton, M. Levitin, 2013, 1303.2185.

Spectral Theory of Laplace and Schrödinger Operators ( 13 w 5059 )

R. Laugesen, I. Polterovich, R. Benguria, 2013 .

Regularized Traces and Taylor Expansions for the Heat Semigroup

I. Polterovich, M. Hitrik, 2001, math/0105163.

Resolvent expansions and trace regularizations for Schrödinger operators

I. Polterovich, M. Hitrik, 2003 .

Multiplicity bounds for Steklov eigenvalues on Riemannian surfaces

I. Polterovich, M. Karpukhin, G. Kokarev, 2012, 1209.4869.

Spectral geometry of the Steklov problem (Survey article)

Iosif Polterovich, Alexandre Girouard, I. Polterovich, 2017 .

On the Hersch-Payne-Schiffer inequalities for Steklov eigenvalues

I. Polterovich, A. Girouard, 2008, 0808.2968.

Heat Invariants of the Steklov Problem

David A. Sher, I. Polterovich, 2013, The Journal of Geometric Analysis.

Heat Invariants of the Steklov Problem

Iosif Polterovich, David A. Sher, I. Polterovich, 2013, 1304.7233.

Shape optimization for low Neumann and Steklov eigenvalues

Iosif Polterovich, Alexandre Girouard, I. Polterovich, 2008, 0811.2617.

Steklov Geometry Processing: An Extrinsic Approach to Spectral Shape Analysis pdf

Yu Wang, Mirela Ben-Chen, Justin Solomon, 2017, ArXiv.

Spectral problems with mixed Dirichlet-Neumann boundary conditions: isospectrality and beyond

N. Nadirashvili, I. Polterovich, M. Levitin, 2004, math/0409154.

Pleijel's nodal domain theorem for free membranes

I. Polterovich, 2008, 0805.1553.

On a characterization of flat metrics on 2-torus

I. Polterovich, 1996 .

Eigenvalues of a One-Dimensional Dirac Operator Pencil

I. Polterovich, D. Elton, M. Levitin, 2013, Annales Henri Poincaré.

The legacy of Vladimir Andreevich Steklov

Iosif Polterovich, Mateusz Kwasnicki, Nikolay Kuznetsov, 2014 .

Eigenvalue inequalities on Riemannian manifolds with a lower Ricci curvature bound

I. Polterovich, G. Kokarev, Asma Hassannezhad, 2015, 1510.07281.

SP ] 2 M ar 2 01 0 EIGENVALUE INEQUALITIES FOR MIXED STEKLOV PROBLEMS

R. Bañuelos, I. Polterovich, B. Siudeja, 2021 .

Heat traces on spheres and combinatorial identities

I. Polterovich, 2001 .

A commutator method for computation of heat invariants

I. Polterovich, 1998, math/9805047.

Agmon-Kannai method for computation of heat invariants

I. Polterovich, 1998 .

Persistent transcendental B\'ezout theorems

L. Polterovich, I. Polterovich, E. Shelukhin, 2023, 2307.02937.

The Steklov spectrum of surfaces: asymptotics and invariants

David A. Sher, I. Polterovich, L. Parnovski, 2013, Mathematical Proceedings of the Cambridge Philosophical Society.