JOURNAL OF DIFFERENTIAL GEOMETRY
Scope & Guideline
Exploring innovative paths in mathematical research.
Introduction
Aims and Scopes
- Differential Geometry and Topology:
The journal publishes research that explores the geometric properties of differentiable manifolds, including their topological aspects, curvature, and global geometric structures. - Geometric Analysis:
It includes studies that utilize analytical techniques to solve geometric problems, such as the study of minimal surfaces, harmonic maps, and curvature flows. - Mathematical Physics:
Papers often bridge the gap between mathematics and theoretical physics, particularly in areas like gauge theory, string theory, and general relativity. - Complex Geometry:
Research focusing on the geometry of complex manifolds, including Kähler metrics, Calabi-Yau varieties, and holomorphic curves, is a significant theme in the journal. - Algebraic Geometry and Symplectic Geometry:
The journal also features contributions that connect algebraic geometry with differential geometry, particularly in the context of moduli spaces and symplectic structures. - Mathematical Methods in Geometry:
Innovative methodologies for solving geometric problems, including variational methods, min-max theory, and spectral analysis, are frequently discussed.
Trending and Emerging
- Geometric Flows:
An increasing number of papers are dedicated to studying various geometric flows, such as mean curvature flow and Ricci flow, showcasing their applications in understanding the evolution of geometric structures. - Mirror Symmetry and String Theory:
The intersection of differential geometry with string theory, particularly through mirror symmetry and the study of Calabi-Yau manifolds, is gaining substantial attention, reflecting broader interests in mathematical physics. - Applications of Topological Methods:
There is a growing trend in applying topological concepts and techniques, such as persistent homology and other invariants, to tackle problems in geometry and analysis. - Higher-Dimensional Geometry:
Research focusing on the geometric properties of higher-dimensional manifolds is becoming more prominent, indicating a shift towards understanding complex structures in higher dimensions. - Nonlinear PDEs in Geometry:
The use of nonlinear partial differential equations to address geometric problems, particularly in complex and algebraic geometry, is increasingly prevalent in recent publications.
Declining or Waning
- Classical Differential Geometry:
Papers focusing on classical results and techniques in differential geometry, such as those related to curves and surfaces, have become less common as more advanced topics gain traction. - Elementary Methods in Geometry:
There has been a noticeable reduction in contributions that rely on basic geometric techniques, as the field increasingly favors more sophisticated analytical or algebraic approaches. - Non-Smooth Geometries:
Research on non-smooth geometrical constructs, such as singular spaces or fractals, appears to be diminishing in favor of studies on smooth manifolds and their properties.
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