Spherical soap bubbles, isometric minimal immersions of round spheres into round spheres, or spherical immersions for short, belong to a fast growing and fascinating area between algebra and geometry.
Spherical soap bubbles, isometric minimal immersions of round spheres into round spheres, or spherical immersions for short, belong to a fast growing and fascinating area between algebra and geometry. In this accessible book, the author traces the development of the study of spherical minimal immersions over the past 30 plus years, including a valuable selection of exercises.
From the reviews of the first edition:
This monograph is devoted to minimal immersions between round spheres. ... Indeed, the author's exposition is largely self-contained - and leisurely. Exercises are abundant, forming an integral part of the presentation. ... This monograph has been written with great care. It would be appropriate for an undergraduate or graduate seminar. (J. Ells, Mathematical Reviews, Issue 2002 i)
In this book, the author traces the development of the study of spherical minimal immersions over the past 30-plus years ... . In trying to make this monograph accessible not just to research mathematicians but to mathematics graduate students as well, the author included sizeable pieces of material from upper-level undergraduate courses, additional graduate level topics such as Felix Klein's classical treatise of the icosahedron, and a valuable selection of exercises. (L'Enseignement Mathematique, Vol. 48 (1-2), 2002)
This very interesting monograph for researchers and graduate students as well, gives a wide picture of the theory of spherical soap bubbles, which studies isometric minimal immersions of round spheres ... . Each chapter ends with some additional topics and some challenging problems. A useful appendix with some basic notions is given at the end of the book. (Cornelia-Livia Bejan, Zentralblatt MATH, Vol. 1074, 2005)