World's Best Scientists 2026 revealed!

D-Index & Metrics

Mathematics

D-Index
46
Citations
8233
World Ranking
1365
National Ranking
610

Rupert L. Frank publication distribution in Mathematics in 2026

The chart shows the distribution of publications by all Research.com ranked scientists in the field of Mathematics in 2026. The highlighted bar marks where Rupert L. Frank sits on this spectrum.

42–46 publications: 3 scientists 47–51 publications: 5 scientists 52–56 publications: 7 scientists 57–61 publications: 20 scientists 62–66 publications: 14 scientists 67–71 publications: 25 scientists 72–76 publications: 19 scientists 77–81 publications: 35 scientists 82–86 publications: 50 scientists 87–91 publications: 60 scientists 92–96 publications: 86 scientists 97–101 publications: 84 scientists 102–106 publications: 83 scientists 107–111 publications: 90 scientists 112–116 publications: 99 scientists 117–121 publications: 90 scientists 122–126 publications: 91 scientists 127–131 publications: 109 scientists 132–136 publications: 110 scientists 137–141 publications: 98 scientists 142–146 publications: 112 scientists 147–151 publications: 102 scientists 152–156 publications: 88 scientists 157–161 publications: 106 scientists 162–166 publications: 83 scientists 167–171 publications: 102 scientists 172–176 publications: 77 scientists 177–181 publications: 81 scientists 182–186 publications: 78 scientists 187–191 publications: 71 scientists 192–196 publications: 92 scientists 197–201 publications: 64 scientists 202–206 publications: 69 scientists 207–211 publications: 64 scientists 212–216 publications: 62 scientists 217–221 publications: 58 scientists 222–226 publications: 53 scientists 227–231 publications: 50 scientists 232–236 publications: 46 scientists 237–241 publications: 46 scientists 242–246 publications: 46 scientists 247–251 publications: 43 scientists 252–256 publications: 29 scientists 257–261 publications: 45 scientists 262–266 publications: 30 scientists 267–271 publications: 33 scientists 272–276 publications: 34 scientists 277–281 publications: 30 scientists 282–286 publications: 31 scientists 287–291 publications: 21 scientists 292–296 publications: 34 scientists 297–301 publications: 26 scientists 302–306 publications: 10 scientists 307–311 publications: 17 scientists 312–316 publications: 23 scientists 317–321 publications: 13 scientists 322–326 publications: 16 scientists 327–331 publications: 26 scientists 332–336 publications: 13 scientists 337–341 publications: 13 scientists 342–346 publications: 16 scientists 347–351 publications: 17 scientists 352–356 publications: 12 scientists 357–361 publications: 18 scientists 362–366 publications: 18 scientists 367–371 publications: 9 scientists 372–376 publications: 11 scientists 377–381 publications: 8 scientists 382–386 publications: 8 scientists 387–391 publications: 9 scientists 392–396 publications: 9 scientists 397–401 publications: 8 scientists 402–406 publications: 11 scientists 407–411 publications: 6 scientists 412–416 publications: 6 scientists 417–421 publications: 9 scientists 422–426 publications: 8 scientists 427–431 publications: 5 scientists 432–436 publications: 8 scientists 437–441 publications: 8 scientists 442–446 publications: 4 scientists 447–451 publications: 4 scientists 452–456 publications: 4 scientists 457–461 publications: 2 scientists 462–466 publications: 2 scientists 467–471 publications: 4 scientists 472–476 publications: 3 scientists 477–481 publications: 3 scientists 482–486 publications: 6 scientists 487–491 publications: 3 scientists 492–496 publications: 5 scientists 497–501 publications: 5 scientists 502–506 publications: 1 scientists 507–511 publications: 6 scientists 512–516 publications: 4 scientists 517–521 publications: 1 scientists 522–526 publications: 3 scientists 527–531 publications: 1 scientists 532–536 publications: 4 scientists 537+ publications: 100 scientists
42 publications 537+

This scientist: 217 publications — 68th percentile

68% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 537 publications or more.

Rupert L. Frank D-index placement in Mathematics in 2026

The chart shows the D-index (discipline H-index) distribution of Mathematics scientists ranked by Research.com in 2026. The highlighted bar marks where Rupert L. Frank sits on this spectrum.

30 D-Index: 174 scientists 31 D-Index: 151 scientists 32 D-Index: 174 scientists 33 D-Index: 117 scientists 34 D-Index: 136 scientists 35 D-Index: 127 scientists 36 D-Index: 145 scientists 37 D-Index: 153 scientists 38 D-Index: 150 scientists 39 D-Index: 150 scientists 40 D-Index: 138 scientists 41 D-Index: 136 scientists 42 D-Index: 93 scientists 43 D-Index: 108 scientists 44 D-Index: 115 scientists 45 D-Index: 112 scientists 46 D-Index: 103 scientists 47 D-Index: 75 scientists 48 D-Index: 59 scientists 49 D-Index: 67 scientists 50 D-Index: 60 scientists 51 D-Index: 57 scientists 52 D-Index: 59 scientists 53 D-Index: 62 scientists 54 D-Index: 60 scientists 55 D-Index: 50 scientists 56 D-Index: 42 scientists 57 D-Index: 54 scientists 58 D-Index: 50 scientists 59 D-Index: 42 scientists 60 D-Index: 41 scientists 61 D-Index: 35 scientists 62 D-Index: 40 scientists 63 D-Index: 21 scientists 64 D-Index: 31 scientists 65 D-Index: 27 scientists 66 D-Index: 29 scientists 67 D-Index: 19 scientists 68 D-Index: 25 scientists 69 D-Index: 17 scientists 70 D-Index: 18 scientists 71 D-Index: 12 scientists 72 D-Index: 14 scientists 73 D-Index: 13 scientists 74 D-Index: 18 scientists 75 D-Index: 9 scientists 76 D-Index: 11 scientists 77 D-Index: 10 scientists 78 D-Index: 9 scientists 79 D-Index: 16 scientists 80 D-Index: 12 scientists 81 D-Index: 10 scientists 82 D-Index: 5 scientists 83 D-Index: 5 scientists 84 D-Index: 13 scientists 85 D-Index: 6 scientists 86+ D-Index: 99 scientists
30 D-Index 86+

This scientist: 46 D-Index — 64th percentile

64% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 86 D-Index or more.

Overview

Rupert L. Frank is affiliated with the California Institute of Technology in the United States. Their work primarily spans the field of Mathematics, with a focus on subfields including Mathematical Physics, Applied Mathematics, Computational Theory and Mathematics, Atomic and Molecular Physics and Optics, as well as Geometry and Topology.

The main research topics addressed by Rupert L. Frank include:

  • Spectral Theory in Mathematical Physics
  • Nonlinear Partial Differential Equations
  • Advanced Mathematical Modeling in Engineering
  • Numerical Methods in Inverse Problems
  • Advanced Mathematical Physics Problems
  • Advanced Harmonic Analysis Research
  • Graph Theory and Applications

Their recent scholarly output includes the following papers:

  • The Lieb-Thirring inequalities: Recent results and open problems, 2021, Proceedings of Symposia in Pure Mathematics
  • Classification of solutions of an equation related to a conformal log Sobolev inequality, 2020, Advances in Mathematics
  • Quantum Corrections to the Pekar Asymptotics of a Strongly Coupled Polaron, 2020, Communications on Pure and Applied Mathematics
  • Non-degeneracy for the critical Lane-Emden system, 2021, IRIS Research product catalog (Sapienza University of Rome)
  • Degenerate stability of some Sobolev inequalities, 2022, Annales de l'Institut Henri Poincaré C Analyse Non Linéaire

Rupert L. Frank frequently collaborates with the following co-authors:

  • Ари Лаптев
  • Simon Larson
  • Timo Weidl
  • Tobias König
  • Michael Loss

The scholar publishes regularly in several venues, notably including:

  • arXiv (Cornell University)
  • Journal of Functional Analysis
  • Advances in Mathematics
  • Calculus of Variations and Partial Differential Equations
  • Journal of the European Mathematical Society

Rupert L. Frank also contributes to academic book publications with works released through multiple presses:

  • EMS Press eBooks: The Physics and Mathematics of Elliott Lieb (2022)
  • Cambridge University Press: Schrödinger Operators: Eigenvalues and Lieb-Thirring Inequalities (2022)
  • EMS series of congress reports: Partial Differential Equations, Spectral Theory, and Mathematical Physics (2021)
  • Springer Nature: Geometric and Analytic Aspects of Functional Variational Principles (2024)

Best Publications

  • Uniqueness of Radial Solutions for the Fractional Laplacian

    Rupert L. Frank;Enno Lenzmann;Luis Silvestre

  • Non-linear ground state representations and sharp Hardy inequalities

    Rupert L. Frank;Robert Seiringer

  • Uniqueness of non-linear ground states for fractional Laplacians in ${\mathbb{R}}$

    Rupert L. Frank;Rupert L. Frank;Enno Lenzmann;Enno Lenzmann

  • Monotonicity of a relative R'enyi entropy

    Rupert L. Frank;Elliott H. Lieb

  • Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators

    Rupert L. Frank;Rupert L. Frank;Elliott H. Lieb;Robert Seiringer

  • Uniqueness and Nondegeneracy of Ground States for $(-\Delta)^s Q + Q - Q^{lpha+1} = 0$ in $\mathbb{R}$

    Rupert L. Frank;Enno Lenzmann

  • Monotonicity of a relative Rényi entropy

    Rupert L. Frank;Elliott H. Lieb

  • Sharp constants in several inequalities on the Heisenberg group

    Rupert L. Frank;Elliott H. Lieb

  • Eigenvalue bounds for Schr"odinger operators with complex potentials

    Rupert L. Frank

  • Eigenvalue bounds for Schrödinger operators with complex potentials

    Rupert L. Frank

  • Restriction theorems for orthonormal functions, Strichartz inequalities, and uniform Sobolev estimates

    Rupert L. Frank;Julien Sabin

  • Inversion positivity and the sharp Hardy–Littlewood–Sobolev inequality

    Rupert L. Frank;Elliott H. Lieb

  • A New, Rearrangement-free Proof of the Sharp Hardy–Littlewood–Sobolev Inequality

    Rupert L. Frank;Elliott H. Lieb

  • Lieb–Thirring Inequalities for Schrödinger Operators with Complex-valued Potentials

    Rupert L. Frank;Ari Laptev;Elliott H. Lieb;Robert Seiringer

  • Intrinsic metrics for non-local symmetric Dirichlet forms and applications to spectral theory

    Rupert L. Frank;Daniel Lenz;Daniel Wingert

  • The sharp constant in the Hardy-Sobolev-Maz'ya inequality in the three dimensional upper half-space

    Rafael D. Benguria;Rupert L. Frank;Michael Loss

  • Maximizers for Gagliardo–Nirenberg inequalities and related non-local problems

    Jacopo Bellazzini;Rupert L. Frank;Nicola Visciglia

  • A Compactness Lemma and Its Application to the Existence of Minimizers for the Liquid Drop Model

    Rupert L. Frank;Elliott H. Lieb

  • Remainder terms in the fractional Sobolev inequality

    Shibing Chen;Rupert L. Frank;Tobias Weth

  • Eigenvalue bounds for Schrödinger operators with complex potentials. III

    Rupert L. Frank

  • The Critical Temperature for the BCS Equation at Weak Coupling

    Rupert L. Frank;Christian Hainzl;Serguei Naboko;Robert Seiringer

Frequent Co-Authors

Elliott H. Lieb
Elliott H. Lieb Princeton University
Eric A. Carlen
Eric A. Carlen Rutgers, The State University of New Jersey
Barry Simon
Barry Simon California Institute of Technology
Michael Loss
Michael Loss Georgia Institute of Technology
Jan Philip Solovej
Jan Philip Solovej University of Copenhagen
Benjamin Schlein
Benjamin Schlein University of Zurich
Jean Dolbeault
Jean Dolbeault Paris Dauphine University
Luis Silvestre
Luis Silvestre University of Chicago
Angela Pistoia
Angela Pistoia Sapienza University of Rome
Daniel Lenz
Daniel Lenz Friedrich Schiller University Jena

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