Recent Advances Involving Interfaces and Boundaries in Geometric Analysis and Applications
A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Geometry and Topology".
Deadline for manuscript submissions: 31 January 2026
Special Issue Editor
Interests: geometric measure theory; calculus of variations; convexity; anisotropic perimeter; lower semicontinuity; existence of energy minimizers; boundary regularity; geometric optimization problems; geometric evolution problems; curvature flows; isoperimetric problems; total variation minimization; crystals; partitions; polycrystals; materials science; image processing; image classification; probability inequalities
Special Issue Information
Dear Colleagues,
This Special Issue is devoted to "Recent Advances Involving Interfaces and Boundaries in Geometric Analysis and Applications". It will provide an opportunity to present recent developments in the theory of static and dynamical problems involving interfaces and boundaries, in addition to their applications in materials science, image processing, medicine, and other fields.
This Special Issue will address the following non-exhaustive, non-mutually exclusive list of topics:
- Geometric evolution problems;
- Free discontinuity problems;
- Prescribed mean curvature problems;
- Total variation minimization;
- Mean curvature flows and related flows;
- Gradient flows;
- Willmore flows;
- Crystalline curvature flows;
- Evolution problems involving networks;
- Analysis of multiple junctions;
- Isoperimetric problems;
- Anisotropic perimeter;
- Fractional perimeters;
- Cheeger sets and Cheeger constants;
- Partitions and clusters;
- Geometric measure theory and variational problems;
- Semicontinuity and existence of minimizers;
- Almost minimal sets;
- Boundary regularity;
- Applications of these areas to materials science, image processing, medicine, or other fields.
The Special Issue is open to receiving further ideas, apart from the aforementioned topics.
We hope that this initiative will be attractive to experts who work in these areas and in their applications. We encourage you to submit your current research for consideration of inclusion in the Special Issue.
Dr. David Caraballo
Guest Editor
Manuscript Submission Information
Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.
Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.
Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.
Keywords
- interface evolution problems
- geometric optimization problems
- energy minimizers
- curvature
- anisotropy
- convexity
- partitions
- networks and multiple junctions
- geometric analysis
- geometric measure theory
- calculus of variations
- materials science
- image processing
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