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Scope & Guideline
Empowering professionals with vital insights in cardiology.
Introduction
Aims and Scopes
- Mathematical Analysis and Partial Differential Equations:
The journal publishes research that delves into various aspects of mathematical analysis, particularly focusing on partial differential equations (PDEs) and their qualitative properties. - Geometric Analysis and Metric Spaces:
Research concerning the geometry of spaces, including studies on curvature, geodesic completeness, and properties of metric spaces, is a core area of the journal. - Sobolev Spaces and Functional Analysis:
The journal emphasizes work related to Sobolev spaces, including the study of Sobolev maps, embeddings, and regularity issues in various settings. - Measure Theory and Integration:
Articles frequently explore measures in different contexts, including Carnot groups and weighted spaces, contributing significant insights into measure theory. - Geometric Flows and Curvature Problems:
The journal features studies on geometric flows, such as mean curvature flows and Ricci flows, particularly in the context of Riemannian and Finsler manifolds.
Trending and Emerging
- Advanced Metric Geometry:
There has been a notable increase in research focused on advanced topics in metric geometry, including Gromov-Hausdorff limits and quasiconformal mappings, indicating a growing interest in the geometric structure of spaces. - Nonlinear Analysis and Critical Equations:
The emergence of papers addressing critical and nonlinear PDEs, such as Choquard-Kirchhoff equations, suggests a rising trend in exploring complex behaviors of solutions to these equations. - Analytical Techniques in Geometric Flows:
Recent articles have focused on analytical approaches to understanding geometric flows, highlighting their relevance in both theoretical research and applied mathematics. - Sobolev Spaces in Non-standard Settings:
There is an increasing focus on Sobolev spaces in non-standard contexts, particularly those involving variable exponents and anisotropic settings, reflecting a trend towards more generalized and applicable mathematical frameworks.
Declining or Waning
- Classical Functional Inequalities:
Although previously a focus area, the publication of papers specifically addressing classical functional inequalities, such as isoperimetric inequalities, has decreased, suggesting a potential shift towards more modern and complex inequalities. - Basic Topological Methods in Analysis:
There seems to be a decline in papers that utilize foundational topological methods, indicating a movement towards more specialized and advanced techniques in analysis. - Elementary Geometric Properties:
Research centered on elementary geometric properties of spaces appears to be waning, as more complex geometric analyses take precedence.
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