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We extend the theory of complete minimal surfaces in $\mathbb{R}^3$ of finite total curvature to the wider class of elliptic special Weingarten surfaces of finite total curvature; in particular, we extend the seminal works of L. Jorge and W. Meeks and R. Schoen. Specifically, we extend the Jorge-Meeks formula relating the total curvature and the topology of the surface and we use it to classify planes as the only elliptic special Weingarten surfaces whose total curvature is less than $4 ��$. Moreover, we show that a complete (connected), embedded outside a compact set, elliptic special Weingarten surface of minimal type in $\mathbb{R}^3$ of finite total curvature and two ends is rotationally symmetric; in particular, it must be one of the rotational special catenoids described by R. Sa Earp and E. Toubiana. This answers in the positive a question posed in 1993 by R. Sa Earp. We also prove that the special catenoids are the only connected non-flat special Weingarten surfaces whose total curvature is less than $8 ��$., 41 pages, 15 figures

We performed a detailed morphologic, immunophenotypic, and endocrine characterization of neoplastic and non-neoplastic lesions of androgen-producing cells known to harbor or lack Reinke crystals (RCs) with an aim to provide further insight into the nature of these cells and crystals. Study cases were selected from the files of participating hospitals and subclassified according to current classifications: 20 with Leydig cell tumors (LCTs), 2 with testicular adrenal rest tumors (TARTs), 2 with testicular tumors of adrenogenital syndrome (TTAGS), and 2 with androgen insensitivity syndrome (AIS). An extensive immunophenotypic panel including markers used in sex cord-stromal cell tumors, androgen hormones, enzymes, and receptors was applied to the cases and 10 non-tumoral adrenal glands. Non-tumoral tissues were scored separately. RCs were present in 90 % of LCTcases and all cases with normal Leydig cells; RCs stained specifically with calretinin and 3β-hydroxysteroid dehydrogenase (3BHSD) and were present only in cells with high concomitant expression of both proteins, a phenotype unique to Leydig cells and LCTs. Leydig cells from AIS cases lack RCs due to decreased expression of 3BHSD. Calretinin is decreased in testicular adrenal-like tumors and absent in normal adrenocortical cells, which explain why they lack RCs. Calretinin expression in androgen-producing cells is independent from androgen receptors and androgen synthesis. RCs represent for the most part, if not exclusively, crystallized forms of a 3BHSD/calretinin complex. Androgen-producing cells containing and lacking RCs differ mainly in the level of expression of these proteins and androgen receptors.

Reinke crystals (RC) are pathognomonic of Leydig cells (LCs); they are thought to be rare in normal testes and to occur only in approximately one third of LC tumors. We noticed that crystals present in touch imprint and frozen sections of an LC tumor disappeared after tissue fixation. This phenomenon led us to hypothesize that their reported low frequency in normal and neoplastic LCs may be secondary to degradation/dissolution of the crystals after formalin fixation. Our review of the literature also led us to hypothesize that RC are better preserved after air-drying and alcohol fixation. We collected testicular samples from 21 autopsies including air-dried cytologic preparations and tissue samples that were fixed in alcohol or formalin. We found that RC are common in normal LC but dissolve rapidly in formalin and slowly and only partially in alcohol. The composition of RC is unknown; however, they have been reported to stain specifically for nestin, an intermediate filament expressed mainly in neural and muscle tissue. Because the crystals have only been described in androgen-producing cells, we hypothesized that the crystals may represent a crystallized form of androgenic hormones, hormone complexes, or enzymes involved in their synthesis. We performed immunostains for androgens and enzymes involved in androgenesis. We also performed nestin immunostain to confirm the previous study. The crystals stain specifically with antibodies anti-3β-hydroxysteroid dehydrogenase and are negative for the remaining androgenic enzymes, androgenic hormones, and nestin.