Preprints and publications:

(with R. Gabdurakhmanov)
On Calderon's problem for the connection Laplacian. arXiv:2112.13419

Berger's inequality in the presence of upper sectional curvature bound. IMRN, to appear. Based on arXiv:1910.06647

Bounds for Laplace eigenvalues of Kaehler metrics. Adv. Math. 365 (2020), to appear. arXiv:1801.02276

Conformal volume and eigenvalue problems. Indiana Univ. Math. J. 69 (2020), 19752003. arXiv:1712.08150

(with A. Hassannezhad, I. Polterovich)
Eigenvalue inequalities on Riemannian manifolds with a lower Ricci curvature bound. Yuri Safarov's memorial volume. J. Spectr. Theory 16 (2016), 807835. arXiv:1510.07281

(with V. Apostolov, D. Jakobson)
An extremal eigenvalue problem in Kahler geometry.
Paul Gauduchon's anniversary volume. J. Geom. Phys. 91 (2015), 108116.
arXiv:1411.7725

(with A. Hassannezhad)
SubLaplacian eigenvalue bounds on subRiemannian manifolds. Ann. Scuola Norm. Sup. Pisa Cl. Sci.(5) 16 (2016), 10491092. arXiv:1407.0358

On multiplicity bounds for Schrodinger eigenvalues on Riemannian surfaces. Anal. PDE 7 (2014), 13971420. arXiv:1310.2207

(with M. Karpukhin, I. Polterovich)
Multiplicity bounds for Steklov eigenvalues on Riemannian surfaces.
Ann. Inst. Fourier 64 (2014), 24812502. arXiv:1209.4869

SubLaplacian eigenvalue bounds on CR manifolds. Comm. Partial Differential Equations 38 (2013), 19711984.
arXiv:1202.5465

Variational aspects of Laplace eigenvalues on Riemannian surfaces.
Adv. Math. 258 (2014), 191239. arXiv:1103.2448

Curvature and bubble convergence of harmonic maps. J. Geom. Anal. 23 (2013), 10581077. arXiv:1005.3783

On the concentrationcompactness phenomenon for the
first Schrodinger eigenvalue.
Calc. Var. Partial Differential Equations 38 (2010), 2943.
arXiv:0904.3264

(with N. Nadirashvili) On the first Neumann eigenvalue bounds
for conformal metrics.
Topics around the Research of Vladimir Maz'ya. II, 229238,
"International Mathematical Series" 12, Springer, 2010.

(with D.Kotschick) Fibrations and fundamental groups of
KaehlerWeyl manifolds.
Proc. Amer. Math. Soc. 138 (2010), 9971010.
arXiv:0811.1952

On geodesic homotopies of controlled width and
conjugacies in isometry groups.
Groups Geom. Dyn. 7 (2013), 911929. PDF arXiv:0709.3469

On pseudoharmonic maps in conformal geometry.
Proc. London Math. Soc. 99 (2009), 168194. Based on the preprint
arXiv:0705.3821

On the topology of the evaluation map and rational
curves.
Internat. J. Math. 19 (2008), 369385.
PDF arXiv:math/0603255

A note on Morse inequalities for harmonic maps with
potential and their applications.
Ann. Global Anal. Geom. 33 (2008), 101113.
PDF

(with S.Kuksin) Quasilinear elliptic differential equations
for mappings of manifolds, II.
Ann. Global Anal. Geom. 31 (2007), 59113.
PDF

Elements of qualitative theory of quasilinear elliptic
partial differential equations for mappings valued in compact
manifolds. PhD Thesis, HeriotWatt University, 2004.

On the compactness property of the quasilinearly
perturbed harmonic map equation.
Sbornik: Mathematics
194 (2003), no. 7, 10551068.
PDF

(with S.Kuksin) Quasilinear elliptic differential equations
for mappings between manifolds, I. (Russian) Algebra i Analiz
15 (2003), no. 4, 160; translation in St.Petersburg
Math. Journal 15 (2004), 469505.

The compactness of the set of solutions of the
quasilinearly perturbed harmonic map equation.
Russian Math. Surveys,
57 (2002), 995996.
