List of papers

This page is last updated on May 29, 2000.

This is the list of my English-language papers. Some of them are available in TeX, DVI, and PostScript formats. PostScript files are ZIP-compessed to save disk space and bandwidth. Use unzip or pkunzip to decompress.

Please note that the papers placed on this page are pre-submitted versions and may differ from the journal publications.

Sergei Ivanov. On two-dimensional minimal fillings. Preprint, 2000.

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This is a draft translation from Russian. The Russian version will be published in Algebra i Analiz, vol.12 (2000).

Dmitri Burago, Sergei Ivanov. On asymptotic isoperimetric constant of tori. Geom. Funct. Anal., vol.8 (1998), 783-787

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Sergei Ivanov. A note on converging metrics of curvature bounded above on 2-polyhedra. Submitted to St. Petersburg Math. J.

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This paper is translated from Russian. The Russian version is published in Algebra i Analiz, vol.10 (1998), 783-787.

Sergei Ivanov, Michel de Rougemont. Interactive protocols on the reals. Proc. STACS 98, Lecture Notes in Computer Science, 1373 (1998), 499-510.
Dmitri Burago, Sergei Ivanov, Bruce Kleiner. On the structure of the stable norm of periodic metrics. Math. Research Letters, vol.4 (1997), 791-808.

Abstract. We study the differentiability of the stable norm $|*|$ associated with a $Z^n$-periodic metric on $R^n$. Extending one of the main results of [Bangert2], we prove that if $p\in R^n$ and the coordinates of $p$ are linearly independent over $Q$, then there is a linear 2-plane $V$ containing $p$ such that the restriction of $|*|$ to $V$ is differentiable at~$p$. We construct examples where $|*|$ is not differentiable at a point with coordinates linearly independent over $Q$.

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Sergei Ivanov. Volumes of manifolds in Gromov-Hausdorff convergence. St. Petersburg Math. J., vol.9 (1998), 945-959

Abstract. Let $n\ge 2$, $M$ and $M_k$ ($k=1,2,...$) be compact Riemannian $n$-manifolds, possibly with boundaries, and let $\{M_k\}$ converge to $M$ with respect to the Gromov-Hausdorff distance. We prove that $ Vol(M) \le \liminf Vol(M_k) $ provided that one of the following holds: (1) $M_k$ are homotopy equivalent to $M$, and $M$ admits either a nonzero-degree map onto the torus $T^n$ or an odd-degree map onto $RP^n$; or (2) $n=2$ and the Euler characteristics of $M_k$ are uniformly bounded. For $n\ge 3$ we give examples of convergence in which $M$ and $M_k$ are diffeomorphic to $S^n$ and $Vol(M_k)\to 0$.

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This paper is translated from Russian. The Russian version is published in Algebra i Analiz, vol.9 (1997), no.5, pp.65-83.

Dmitri Burago, Sergei Ivanov. On asymptotic volume of tori. Geom. Funct. Anal., vol.5 (1995), 800-808

A rough formulation of the main result: in the universal cover of a Riemannian n-torus, the volumes of metric balls with radii going to infinity grow (asymtotically) at least as fast as they do in R^n; and the equality holds only for flat metrics.

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Dmitri Burago, Sergei Ivanov. Riemannian tori without conjugate points are flat. Geom. Funct. Anal., vol.4 (1994), 259-269

This is the original proof of the E.Hopf conjecture about tori without conjugate points.

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Dmitri Burago, Sergei Ivanov. Isometric embeddings of Finsler manifolds. Algebra i Analiz, vol.5 (1993), 179-192 (Russian); St.Petersburg Math. J., vol.5 (1994), 159-169 (English).

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