Symmetry in Differential Geometry and Geometric Analysis

Dear Colleagues,

Fractal geometry is an important branch of mathematics that allows for the description of sets that are too intricate to fit into classical geometry. The concept of fractals was first introduced by Mandelbrot in the 1970s as a class of highly irregular sets usually presenting with self-similarity, infinite complexity, and a non-integral fractal dimension. Up to now, it has been hugely significant for the development of a variety of sciences. In mathematics, fractals originate from chaos and dynamic systems. Soon after their discovery, they began to appear in almost every field and can be systematically studied using classical and modern methods. In recent years, scholars have mainly focused on the following research objects: fractal dimensions of graphs, fractal interpolation and approximation, fractals and dynamical systems, self-similarity and Lipschitz equivalence, geometric measure theory, fractional calculus of fractal functions, fractal geometry, number theory, etc. In addition, fractals have been widely applied in other academic fields, such as physics, statistics, geology, material science, quantization theory, signal processing, computer image processing, pattern recognition, and more. Therefore, fractal geometry has increasingly shown its tremendous research value for both real life and scientific development.

It is well known that fractals are widely distributed in nature, such as mountains, landforms, cloud clusters, and so on. Mandelbrot once said that fractal geometry is the language of nature. There exist a lot of symmetries in natural objects with fractal characteristics, of which the most prominent one might be the Koch snowflake. Therefore, it is of great interest to explore the phenomena of symmetry or asymmetry in the fractal world.

This Special Issue aims to collect a series of high-quality papers from renowned experts from around the world to present the latest research on fractal geometry and its various applications. While the focus of this issue includes all the aspects mentioned above, we particularly welcome contributions from researchers who use the concepts of symmetry or asymmetry in their methodologies.

Dr. Yongshun Liang
Dr. Saurabh Verma
Dr. Arulprakash Gowrisankar
Guest Editors

Manuscript Submission Information

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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. Symmetry 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.