Isoperimetric Inequalities in Riemannian Manifolds
暫譯: 黎曼流形中的等周不等式

本書對黎曼流形中的等周不等式提供了一個連貫的介紹，涵蓋了過去25年來獲得的許多結果，並討論了該領域中的不同技術。書中以清晰且吸引人的風格撰寫，包含足夠的入門材料，使其對研究生也具可讀性。對於從幾何或分析的角度研究幾何不等式的研究人員，以及對將所描述的技術應用於其領域感興趣的人士，本書都將具有吸引力。

Manuel Ritoré is professor of Mathematics at the University of Granada since 2007. His earlier research focused on geometric inequalities in Riemannian manifolds, specially on those of isoperimetric type. In this field he has obtained some results such as a classification of isoperimetric sets in the 3-dimensional real projective space; a classification of 3-dimensional double bubbles; existence of solutions of the Allen-Cahn equation near non-degenerate minimal surfaces; an alternative proof of the isoperimetric conjecture for 3-dimensional Cartan-Hadamard manifolds; optimal isoperimetric inequalities outside convex sets in the Euclidean space; and a characterization of isoperimetric regions of large volume in Riemannian cylinders, among others. Recently, he has become interested on geometric variational problems in spaces with less regularity, such as sub-Riemannian manifolds or more general metric measure spaces, where he has obtained a classification of isoperimetric sets inthe first Heisenberg group under regularity assumptions, and Brunn-Minkowski inequalities for metric measure spaces, among others.

曼努埃爾·里托雷自2007年起擔任格拉納達大學的數學教授。他早期的研究專注於黎曼流形中的幾何不等式，特別是與等周型有關的問題。在這個領域，他獲得了一些成果，例如對三維實射影空間中的等周集合進行分類；三維雙氣泡的分類；在非退化最小曲面附近的艾倫-卡恩方程的解的存在性；對三維卡坦-哈達馬流形的等周猜想的替代證明；在歐幾里得空間中凸集外的最佳等周不等式；以及對黎曼圓柱中大體積等周區域的特徵描述等。最近，他對在較少正則性的空間中的幾何變分問題產生了興趣，例如亞黎曼流形或更一般的度量測度空間，在這些空間中，他在正則性假設下對第一海森堡群中的等周集合進行了分類，並對度量測度空間提出了布倫-明科夫斯基不等式等。