I have a few these plants i think they are really low maintenance and serve as border/edging and no invasive, in my experience, i have use them in sunny/ partial sun, partial shade to deep shade and they are very adaptable in different types of soil and also quite drought tolerance.

1-2 Japanese sedge " ice dance " ( carex " ice dance ") this grass like plants are actually an evergreen in warmer region, they perform well if you have enough moisture, but they also grow under my silver maple and juniper, forsythia, oaks .you know how taught to grow under a big tree. they will grow well in morning sun and afternoon shade, but it doesn't matter as long as there are some moisture, they can survive. 3. Another Japanese sedge " kaga nishiki" ( carex " kaga nishiki / gold fountain)very attractive bright and gold/green variegated fine foliage and also very adaptable , i have used it in a shade and dry area , hardy water, as long as the soil is deep and they don't mind clay .

4 &5 Geranium Cambridge or geranium cantabrigiense, I call them little pink geranium, this is one of my favorite ground cover for little garden site , especially under a standard looking small tree ( like hydrangea, service berry , lilacs ) or a pole, mailbox , birdbath, or a tree stump, you want to make it look pretty and natural in a square corner, or a long walkway but not much soil, they basically don't need much soil , and they can easily remove or just cutting the stems and stuck in a moist top soil and start rooting, they can grow in full sun and shade , will change the color of leaves with seasons interest and have pink little flowers in spring, and I don't need to do anything but water if water gets hot once a week. They over winter easily don't need any protection and grow fast and cover up the place you need .

6&7 Big root geranium ( geranium macrorhizum) this is another perennial I use it in a place with the less care but taught and can't water or enough sun area, like a garden I help with a Norwegian maple and linden and after I pull out all the ivy and periwinkle, they spread fast, sun or shade , as long as it is a cool condition on the ground ( give them tree leaves in fall just cover them ) and water every two week, they are fine and they also has a pink/purple color flowers in spring, they are good looking when you plants in a long path , a big tree , a slope and a corner with a big plants or small tree .

8. Big Lamb Ear - if you want some this silvery, wooly , fluffy and soft plants , I have plenty to give. The real name stachys Byzantina " Helen Von stein" , they look nice when you grow them in a big area, and their leaves also bigger then the original lamb's ear, but they don't flower much like the original one, which is better so they won't flope and leggy, they grow well with variety of soil, and also can tolerate part sun to a bit shade , if you have a slope or a big area want to have a stunning looking, they will look great in a lane way, or a darker background, this plants like clay soil and do well without much water .

9-11creeping phlox. Well this is a sunny ground cover perennial without much care, in Japan they grow mass on a hill side or a slope side and it looks amazing when they bloom, has many colors from white, pink, red, pink , purple, can handle 40 c sun to -40 c freezing and if you want to make it nice, grow them with some rocks, under a sunny side tree or edge and they don't need much care , only water them and give them some soil after bloom and it will look nice in a open area .

Well hopefully will help some people like to have simple plants and low maintenance.

What kind edging between grass and mulched garden bed will require minimal maintenance?

I have Zoysia grass and it annoyingly spreads into garden beds like a weed, requiring regular weedwhacking as well as regular "weed" pulling.