We consider a CMC hypersurface with an isolated singular point at which the tangent cone is regular, and such that, in a neighbourhood of said point, the hypersurface is the boundary of a Caccioppoli set that minimises the standard prescribed-mean-curvature functional. We prove that in a ball centred at the singularity there exists a sequence of smooth CMC hypersurfaces, with the same prescribed mean curvature, that converge to the given one. Moreover, these hypersurfaces arise as boundaries of minimisers. In ambient dimension 8 the condition on the cone is redundant. (When the mean curvature vanishes identically, the result is the well-known Hardt–Simon approximation theorem.
Impact Factor: 1.4
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Advances in Calculus of Variations
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Managing Editors:
Juha Kinnunen
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Editorial Board:
Zoltán Balogh
Language:
English
First published:
January 25, 2008
Publication Frequency:
4 issues per year
About this journal
Objective
Advances in Calculus of Variations publishes high quality original research focusing on that part of calculus of variation and related applications which combines tools and methods from partial differential equations with geometrical techniques.
Topics
- existence and regularity for minimizers and critical points
- variational methods for partial differential equations
- geometrical aspects of calculus of variation: minimal surfaces, harmonic mappings, geometrically motivated flows, curvature equations, quasi-conformal mappings
- applications of variational methods to non-linear elasticity, free boundary problems, general relativity
- geometric measure theory
Article formats
Research articles
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Your benefits:
- Highly specialized journal
- Rigorous and thorough peer-review
- Significant impact factor, highly ranked in Journal Citation Report®
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History
The journal was founded in 2008.
Other publications in the field
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Open AccessSmooth approximations for constant-mean-curvature hypersurfaces with isolated singularitiesOctober 1, 2025
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September 23, 2025
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Requires Authentication UnlicensedA simple proof of the 1-dimensional flat chain conjectureLicensedAugust 29, 2025
| Journal Impact Factor | 1.4 | 2024, Journal Citation Reports (Clarivate, 2025) |
| 5-year Journal Impact Factor | 1.5 | 2024, Journal Citation Reports (Clarivate, 2025) |
| Journal Citation Indicator | 1.07 | 2024, Journal Citation Reports (Clarivate, 2025) |
| CiteScore | 3.2 | 2024, Scopus (Elsevier B.V., 2025) |
| SCImago Journal Rank | 1.534 | 2024, SJR (Scimago Lab, 2025; Data Source: Scopus) |
| Source Normalized Impact per Paper | 1.203 | 2024, CWTS Journal Indicators (CWTS B.V., 2025; Data Source: Scopus) |
| Mathematical Citation Quotient | 1.84 |
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Managing Editors
Juha Kinnunen
Department of Mathematics
Aalto University,
Posfach 11100
00076 Aalto, Finland
E-mail: juha.k.kinnunen@aalto.fi
Verena Bögelein
Department of Mathematics
University of Salzburg
Hellbrunnerstraße 34
5020 Salzburg, Austria
E-mail: verena.boegelein@plus.ac.at
Founding Editors
Prof. Frank Duzaar
Prof. Nicola Fusco
Editorial Board
Zoltán Balogh
Mathematisches Institut (MAI)
Universität Bern
Sidlerstrasse 5
3012 Bern, Switzerland
E-mail: zoltan.balogh@math.unibe.ch
Pierre Cardaliaguet
Ceremade (UMR CNRS 7534)
Université Paris-Dauphine
Place du Maréchal De Lattre De Tassigny
75775 Paris Cedex 16 - France
E-mail: cardaliaguet@ceremade.dauphine.fr
Francesca Da Lio
Department of Mathematics
ETHZ
8092 Zurich, Switzerland
E-mail: francesca.dalio@math.ethz.ch
Gianni Dal Maso
SISSA
Via Beirut 2-4
34014 Trieste, Italy
E-mail: dalmaso@sissa.it
Irene Fonseca
Department of Mathematics
Carnegie Mellon University
Pittsburgh, PA 15213, U.S.A.
E-mail: fonseca@andrew.cmu.edu
Ugo Gianazza
Deparment of Mathematics “F. Casorati”
University of Pavia
Via Ferrata 1
27100 Pavia, Italy
E-mail: gianazza@imati.cnr.it
Hitoshi Ishii
Department of Mathematics
Faculty of Education and Integrated Arts and Sciences
Waseda University
Tokyo 169-8050, Japan
E-mail: hitoshi.ishii@waseda.jp
Jan Kristensen
Mathematical Institute
24-29 St. Giles'
University of Oxford
Oxford OX1 3LB, England
E-mail: kristens@maths.ox.ac.uk
Juan Manfredi
Department of Mathematics
University of Pittsburgh
Pittsburgh, PA 15260, U.S.A.
E-mail: manfredi@pitt.edu
José María Martell
Instituto de Ciencias Matematicas CSIC-UAM-UC3M-UCM
Consejo Superior de Investigaciones Cientificas
C/ Nicolas Cabrera 13-15
28049 Madrid, Spain
E-mail: chema.martell@icmat.es
Giuseppe Mingione
Dipartimento di Matematica
Università di Parma
Parco Area delle Scienze 53/a
Campus
43100 Parma, Italy
E-mail: giuseppe.mingione@unipr.it
Kaj Nyström
Department of Mathematics
Uppsala University
Box 480
751 06 Uppsala, Sweden
E-mail: kaj.nystrom@math.uu.se
Reiner Schaetzle
Universität Tübingen
Mathem. Institut
Auf der Morgenstelle 10
Tübingen, Germany
E-mail: rsch@everest.mathematik.uni-tuebingen.de
Zhongwei Shen
University of Kentucky
Department of Mathematics
737 Patterson Office Tower
Lexington, KY 40506-0027, USA
E-mail: zshen2@uky.edu
Yannick Sire
Johns Hopkins University
Dept. of Mathematics
Baltimore, USA
E-mail: ysire1@jhu.edu
Ulisse Stefanelli
Faculty of Mathematics
University of Vienna
Oskar-Morgenstern-Platz 1
1090 Vienna, Austria
E-mail: ulisse.stefanelli@univie.ac.at
Susanna Terracini
Dipartimento di Matematica "Giuseppe Peano"
UniversitaÌ di Torino, Italia
E-mail: susanna.terracini@unito.it
Yoshihiro Tonegawa
Department of Mathematics
Tokyo Institute of Technology
2-12-1 Ookayama, Meguro-ku,
Tokyo 152-8551, Japan
E-mail: Tonegawa@math.titech.ac.jp
Nizar Touzi
Professor, Applied Mathematics
Centre de Mathématiques Appliquées
Ecole Polytechnique
UMR CNRS 7641
91128 Palaiseau Cedex, France
E-mail: nizar.touzi@polytechnique.edu
Guofang Wang
Mathematisches Institut
Albert-Ludwigs-Universität
Ernst-Zermelo-Str. 1
79104 Freiburg im Breisgau, Germany
E-mail: guofang.wang@math.uni-freiburg.de
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Supplementary Materials
Topics
Journal information
Additional information
eISSN:
1864-8266
Language:
English
Publisher:
De Gruyter
Additional information
First published:
January 25, 2008
Publication Frequency:
4 issues per year
eISSN:
1864-8266
Audience(s) for this journal
Researchers in the field of calculus of variation and related applications
