Mean Curvature Flow Solitons in the Presence of Conformal Vector Fields

In this paper we introduce and study a notion of mean curvature flow soliton in Riemannian ambient spaces general enough to encompass target spaces of constant sectional curvature, Riemannian products or, in increasing generality, warped product spaces. As expected, our definition is motivated by the self-similarity of certain special solutions of the mean curvature flow with respect to the flow generated by a distinguished vector field on the target manifold. Our approach allows us to identify some natural geometric quantities that satisfy elliptic equations or differential inequalities in a simple and manageable form for which the machinery of weak maximum principles is valid. The latter is one of the main tools we apply to derive several new characterizations and rigidity results for mean curvature flow solitons that extend to our much more general setting known properties, for instance, in Euclidean space

Predictors for anastomotic leak, postoperative complications, and mortality after right colectomy for cancer: Results from an international snapshot audit

Background: A right hemicolectomy is among the most commonly performed operations for colon cancer, but modern high-quality, multination data addressing the morbidity and mortality rates are lacking. Objective: This study reports the morbidity and mortality rates for right-sided colon cancer and identifies predictors for unfavorable short-term outcome after right hemicolectomy. Design: This was a snapshot observational prospective study. Setting: The study was conducted as a multicenter international study. Patients: The 2015 European Society of Coloproctology snapshot study was a prospective multicenter international series that included all patients undergoing elective or emergency right hemicolectomy or ileocecal resection over a 2-month period in early 2015. This is a subanalysis of the colon cancer cohort of patients. Main Outcome Measures: Predictors for anastomotic leak and 30-day postoperative morbidity and mortality were assessed using multivariable mixed-effect logistic regression models after variables selection with the Lasso method. Results: Of the 2515 included patients, an anastomosis was performed in 97.2% (n = 2444), handsewn in 38.5% (n = 940) and stapled in 61.5% (n = 1504) cases. The overall anastomotic leak rate was 7.4% (180/2444), 30-day morbidity was 38.0% (n = 956), and mortality was 2.6% (n = 66). Patients with anastomotic leak had a significantly increased mortality rate (10.6% vs 1.6% no-leak patients; p 65 0.001). At multivariable analysis the following variables were associated with anastomotic leak: longer duration of surgery (OR = 1.007 per min; p = 0.0037), open approach (OR = 1.9; p = 0.0037), and stapled anastomosis (OR = 1.5; p = 0.041). Limitations: This is an observational study, and therefore selection bias could be present. For this reason, a multivariable logistic regression model was performed, trying to correct possible confounding factors. Conclusions: Anastomotic leak after oncologic right hemicolectomy is a frequent complication, and it is associated with increased mortality. The key contributing surgical factors for anastomotic leak were anastomotic technique, surgical approach, and duration of surgery