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Is there an English alternative to Blaschke's "Kreis und Kugel"? (As you may guess, "Kreis und Kugel" was not translated.) In other words I am looking for a well written and very elementary book which …

Question. Did you ever see inverse limits to be used (or even seriousely considered) anywhere in metric geometry (but NOT in topology)? The definition of inverse limit for metric spaces is given bel …

Please let me know if the following graphs popped up in some problems. Each of these graphs is described by 5 integers $n_1\geqslant k_1$, $n_2\geqslant k_2$, $l\geqslant 0$. We take two complete gr …

I am looking for a reference to the following result. Let $f:\mathbb R^m\to\mathbb R$ be a convex function. Then $f$ is differentiable at all points of outside of a countable union of $(m-1)$-r …

I would like to have an inverse (or/and) implicite function theorem for DC-functions. It seems that I have right definitions, but I fail to prove it... Definitions: Let $h:\mathbb R^n\to\mathbb R$ …

At the moment I am polishing my lecture notes which in particular cover Alexandrov's existence theorem. Denote by $\mathbf{P}_k$ the space of isometry classes of polyhedral metrics on the $\mathbb S …

Lemma. Suppose $(X,\rho)$ is a complete metric space and $\hat \rho$ is its induced intrinsic metric. Then $(X,\hat \rho)$ is complete. This lemma was essentially proved in [2.3. in Metric minimizing …

I am looking for a reference to the following simple statement; it must be classical. (It is easy to proof, but I want to have a reference.) A metric space $X$ that corresponds to a Riemannian man …

Is it proved that white can guarantee at least draw in chess? A while ago I was told that it was proved using strategy-stealing, but I cannot find a reference. Postscript. Please accept my apology - …

I am looking for the original source of the following well known problem. Seven unit cells of a 8×8-chessboard are infected. In one time unit, the cells with at least two infected neighbors (having a …

First, let me recall the statement of the bow lemma. Let $\gamma_1: [a,b] \to \mathbb{R}^2$ and $\gamma_2: [a,b] \to \mathbb{R}^2$ be two smooth unit-speed curves. Assume $\gamma_1$ and its chord bou …

A metric space $M$ is called two-point homogeneous if for any pair of points $(p,q)$ in $M$ any distance preserving map $f\colon\{p,q\}\to M$ can be extended to an isometry $\bar f\colon M\to M$. The …

I am looking for a reference (better a book) that contain integral Bochner formulas for domains with boundary (I need it for 1-forms and functions only). For example I will need the following formula …

The following theorem is commonly attributed to Jacques Hadamard. Assume $\Sigma$ is a smooth locally convex immersed surface in the Euclidean space. Then $\Sigma$ is embedded and bounds a convex …

I am looking for a reference stating that If a graph $z=f(x,y)$ over a convex domain $D$ is minimal, then it is area-minimizing. 5.4.18 in Federer's "Geometric measure theory" and Lemma 1.1. in …