Mathematical Sciences: Stability Problems In The Theory Of Convex Sets

赫尔穆特·格罗默将对与凸集相关的稳定性问题进行研究。凸集理论中的许多定理表明，在一定条件下，一个物体是一种重要的特殊类型，或者两个物体以特定的方式相互联系。与这样的结果相对应，通常很容易引起相关的稳定性问题。例如，有人可能会问，就等周差而言，物体与球的距离有多近。调查者已经在这个方向上取得了一些进展，特别是在与凸体投影有关的结果方面。他未来的研究将集中在与Brunn-Minkowski定理有关的稳定性问题、对称化过程、内接和外接的物体上。预期的技术将涉及球谐函数和Radon变换的几何自适应。

Helmut Groemer will carry out research into stability problems associated with convex sets. Many theorems in the theory of convex sets state that under certain conditions a body is of an important special type or that two bodies are related to one another in a particular way. Corresponding to such results it is often easy to pose an associated stability problem. For example one might ask how close a body is to being a ball in terms of its isoperimetric deficit. The investigator has already made some progress in this direction notably in the case of results connected with projections of convex bodies. His future research will focus on stability problems associated with the Brunn-Minkowski theorem, symmetrization procedures, inscribed and circumscribed bodies. The anticipated techniques will involve geometric adaptations of spherical harmonics and Radon transforms.