In this paper, we study the evolution of submannifold moving by mean curvature minus a external force field. We prove that the flow has a longtime smooth solution for all time under almost optimal conditions. Those conditions are that the second fundamental form on the initial submanifolds is not too large, the external force field, with its any order derivatives, is bounded, and the field is c...

The report "Multiple Chronic Conditions: A Strategic Framework," which was developed by the U.S. Department of Health & Human Services (HSS), has identified as one of the key goals for improving health and the provision of healthcare for people with multiple chronic conditions "to increase clinical, community and patient-centered research." In their linked commentary of this special journal iss...

We develop further some aspects of the spectral theory of a class of Rie-mannian manifolds introduced by E. B. Davies; in particular we study the best constant in the Hardy Inequality which has become important in spectral theory. One application of this constant has been to a certain type of domain perturbation. This technique is useful when the domain has an irregular boundary and this is the...